# 6th Grade Math Number Sense Word Problems

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# Number Sense Word Problems

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# Sixth Grade: Number Sense Word Problems

Band practice lasted 1 1/4 hours
Band practice lasted 1 1/4 hours. Two thirds of the time was spent ...
If Micheal spent 3/4 of his money
If Micheal spent 3/4 of his money to buy 5/6 of his building ...
Chuck`s class is going on a fieldtrip
Chuck's class is going on a fieldtrip this next Thursday. There are 95 students going on the field trip, and each one is paying their teacher \$3.75...
You have 9/4 cup of jelly worms
You have 9/4 cup of jelly worms and a recipe that calls for 1/2 cup of jelly ...
Mr. Jenkins can dig a ditch
Mr. Jenkins can dig a ditch in one hour less then his son. Working together, they can do the job in 2\3 hour. How long does it take for ...
A 32 foot ramp connects a platform with a sidewalk
A 32 foot ramp connects a platform with a sidewalk that is at ground level. if the platforn is 6 feet above ground ...
3/4 of people use internet
3/4 of people use internet and 9/100 use library. How many times more people use internet
Judy has 8 candy bars
Judy has 8 candy bars. She wants to give 1/3 of a candy bar to everyone in her ...
One pizza has 8 slices
One pizza has 8 slices. Deanna ate 2 ...
A guy wire reaches from the top
A guy wire reaches from the top of a 39.32 ft pole to a point on the ground 15' from the ...
I have 6546/7326 cup of sugar
I have 6546/7326 cup of sugar. i used 4325/7326...
Students were asked to choose their favorite subject. If 1/4 of the students chose history and  3/8 chose ...
A marketing manager travels
A marketing manager travels 1080 miles in a corporate jet and then an additional 240 miles by car.  If the car ride takes one hour longer than the jet ride takes, and if the rate of the jet is 6 times the rate of the ...
Peter took a trip of 7 7/8 miles
Peter took a trip of 7 7/8 miles and used 3 1/2 gallons of gas ...
Use an exponent to write an expression
Use an exponent to write an expression with 5 3s that have a value of zero.
simplifying rational expressions
Mario can do the work in X hours. Luigi takes one more hour than Mario to do the work. Together they finish the work in 100 ...
A tailor needs 32/3 yards of material
A tailor needs 32/3 yards of material to make a ...
Ben is making wooden toys
Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben \$1.80 to make. If he sells the toys for \$3.00 each, how many would he have to sell to make a profit of exactly \$36...
solving inequalities
The sum of 2 consecutive even integers is at most 400...
Cheer practice is 2 1/2 hours long
Cheer practice is 2 1/2 hours long. Cheer practice is split up into two groups, 'cheering and dancing', and 'stunting'...
The 2000 population of Jacksonville, Florida
The 2000 population of Jacksonville, Florida was 736,000 and was increasing at the rate of 1.49% each year. At that ...
There were 108 flowers
There were 108 flowers. 4/9 of the flowers bloomed.
How many did not ...
You deposit \$1500 in an account
You deposit \$1500 in an account that pays 5% interest ...
The coach bought 5 pizzas for the party
The coach bought 5 pizzas for the party. The team members ate 7/8 of ...
Find all sets of three consecutive
Find all sets of three consecutive positive even integers whose sum is less then 30.
The Robinsons family drove
The Robinsons family drove for 4000 miles. This was 4/5 the distance the Jones family ...
Mt. Everest, the highest elevation in Asia
Mt. Everest, the highest elevation in Asia, is 29,029 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 below sea ...
The sum of the squares of the two
The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 times the square of the smaller ...
A driver averaged 50 miles per hour
A driver averaged 50 miles per hour on the round trip between Baltimore and Philadelphia, 100 miles away.  The average speeds for going and returning were x and y miles per hour, respectively. Show that
y=25x/(x-25)
Suppose the Population of D.C.
Suppose the Population of D.C. in January of 2006 was 580,000 and 2 percent of them moved every 6 ...
Three consecutive even integers
Three consecutive even integers are such that the square of the third is 100 more than the square of the ...
If you put 25 cents in a bank
If you put 25 cents in a bank and your money doubles each ...
A grade school is taking a trip
A grade school is taking a trip to the zoo. A parent group of 6 people is responsible for putting together 225 box lunches for the trip. The group hopes to recruit extra people for the task. Write an equation that gives the average number "n" of box lunches made per person as a function of the number "p" of parents that can come in and help complete the task. Then graph the ...
The sum of the squares
The sum of the squares of two consecutive positive numbers is 61...
Terry has 3.5 oz of orange juice
Terry has 3.5 oz of orange juice and 2.098 oz of apple juice. He drinks 2 oz of orange juice and 1.3 oz of apple ...
At a sale this week, a desk is being sold
At a sale this week, a desk is being sold for \$425. This is a 32% discount from the original ...
The total cost of a radio and a camera
The total cost of a radio and a camera is \$1650. If the radio costs 4/7 as much as the ...
Josey is ordering pizza for the classroom
Josey is ordering pizza for the classroom. There are 14 people in the classs. She wants to buy enough pizza so that each person could have 1/3 ...
I bought 3 books from bookstore
I bought 3 books from bookstore for a total of 148 dollars. A Chemistry Book, Math book, and Notebook. The Chemistry book was One and half times more than the Math book and notebook combine. The notebook was 2 ...
A biologist is researching a newly-discovered species
A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.)
The formula for velocity is v = (sqrt. 2gh)...
The tallest structure in the U.S.
The tallest structure in the U.S. is a TV tower in Blanchard, North Dakota.  Its height is 2063 feet.  A 2382-foot length of wire is to be used as a guy wire attached to the top of the ...
Melanie can paint a certain barn
Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2 x days. Write a rational expression for the fraction of the barn tht they complete in one day by working together. Evaluate the expression for x =5
For two consecutive integers
For two consecutive integers, the sum of the larger and five times the smaller
One fourth of the guests gathered in the living room
One fourth of the guests gathered in the living room. What fraction of the guests did not gather in the living ...
Amirah is babysitting
Amirah is babysitting her neighbor's cats for an hour a day. She earned \$100 in 4 ...
A lawnmower uses
A lawnmower uses 0.6 of a gallon of gasoline per hour. How many gallons of gasoline will be used if it takes 2...
Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: w=Cr-2, where C is a constant, and r is the distance that the object is from the center of the earth.

a. Solve the equation  for r.

b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)

c. Use the value of C you found in the previous question to determine how much the object would weigh in

i. Death Valley (282 feet below sea level)

ii. The top of Mt McKinley (20,320 feet above sea level)
The sum of a number and its reciprocal
The sum of a number and its reciprocal is 13/6...
A part of Death Valley, near bad water
A part of Death Valley, near bad water, lies 282 ft below sea ...
Joe has 3 boxes of candles
Joe has 3 boxes of candles. Each box has 4 candels. Another box is not filled fully but has only 2 ...
Boyle`s Law, applied to the amount of gas
Boyle's Law, applied to the amount of gas used in a given experiment at a constant temperature, states that pV = 240 where p is pressure measured in kilopascals and V is volume measured in cubic centimeters.  If a decrease in pressure of 1 kPa produces an increase in volume of 20 cm^3...
A soccer field in a city park is rectangular
A soccer field in a city park is rectangular. The length of the field is 120 yards and the width of the field is 60 ...
A town population is 1000
A town population is 1000 on January 1, 2001. It grows at a constant rate of 2% per ...
multiplying rational expressions
Maria's favorite candy bar has 230 claories. the nutrition label sates that 7/8 of the calories come from ...
Billy wants to put wire around his garden
Billy wants to put wire around his garden to keep his dogs from digging his garden up. If the wire is only sold in whole foot how much wire does he have to by if the area of his garden is 620 sq ...
Rodney is putting away test tubes
Rodney is putting away test tubes in science class. He has 50 test tubes and 12 will fit on each rack. How many rack racks will rodney ...
You had 42 bananas but you ate 7 of ...
James uses 1/3 of his land
James uses 1/3 of his land for growing durians 1/4 for bananas 3/8 for guavas and remaining 9 hectares for ...
Find 3 consecutive even numbers
Find 3 consecutive even numbers where the product of the smaller two numbers is 64 less than the square of the largest number.
The sum of the reciprocals of two consecutive integers
The sum of the reciprocals of two consecutive integers is 15/56...
At a well known university
At a well known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students drive more than 40 miles daily, and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many underrgraduate students as there are graduate ...
Sarah spends 1/4 of her income
Sarah spends 1/4 of her income for transportation, 1/6 of her income for food, and 1/3 of her other income for rent and ...
The strength of a medication over time is represented by the equation y=200(1.5)-x, where x represents the number of hours since the medication was taken and y represents the number of micrograms per milimeter left in in the blood. After 4...
Julia bought 3 boxes of candles
Julia bought 3 boxes of candles. Each box contained 4 candles. She kept 2 candles, gave the rest to Mary and told her to give half of them to ...
Jaime bought a case of concert T-shirts
Jaime bought a case of concert T-shirts for \$450. She kept two for herself and sold the rest for \$560, making a profit of \$10 on each ...
3/8 of the people at a restaurant are adults
3/8 of the people at a restaurant are adults. If there are 90 more children than ...
Jan invested \$3600
Jan invested \$3600, part at 8% and the rest at 7%. If the total income from the investments was \$274...
Mary had 10 balloons. She colored 2/5 of them ...
The sum of the reciprocal of 2 consecutive even integers
The sum of the reciprocal of 2 consecutive even integers is 13/84. find these integers
3 3/4 hours to travel
3 3/4 hours to travel from Laketon to High Falls. If you leave Laketon at 10:25...
Jamie buys a square tablecloth. The package label declares, the area of the cloth is 800 sq inches. What is the length of a side of the ...
The first 1/5 mile path
The first 1/5 mile path of a 3/4 mile path through a rose garden is paved with ...
An advertising company designs a campaign
An advertising company designs a campaign to introduce a new product to a metropolitan
area of population M = 3 millions. Let P = P(t) denote the number of people who become aware of
the product by time t. Suppose that P increases at a rate proportional to the number of
people still unaware of the product. The company determines that no one is aware of the
product at the beginning of the campaign and that 40% of the people were
aware of the product after 10 days of ...
If the square root of 2 is less than 6 times a number
If the square root of 2 is less than 6 times a number is divided by 2 less than the number, the quotient is 2...
You want to make a square pillow
You want to make a square pillow. You have 729 square inches of material for the front of the pillow. If you use all the ...
A motorboat travels 30 miles
A motorboat travels 30 miles up a river and returned a distance of 27 miles. The entire trip takes 5 hours. If the rate of the motorboat in still water is 12 ...
I am a two-place decimal that is grater than
I am a two-place decimal that is grater than 80%.  Both of my non-zero digits are different even numbers greater than 5...
Suppose that x mL of pure acid
Suppose that x mL of pure acid are added to 130 mL of a 40% acid ...
The rat population in a major metropolitan city
The rat population in a major metropolitan city is given by the formula n(t)= 73 e0.015 t where t is measured in years since 1990 and n(t) is measured in millions.

What was the rat population in 1990 ...
A rectangle is 7 times as long as it is ...
The additive inverse of a number
The additive inverse of a number divided by twelve is the same as one less than three times its ...
it takes three hours for a pipe
it takes three hours for a pipe to fill a tank of water if the tank does not leak. Our tank has a crack that draines the tank in 5 ...
Cindy has a piece of ribbon
Cindy has a piece of ribbon that is 4/5 of a foot ...
After spending 1/3 of his weekly salary
After spending 1/3 of his weekly salary on groceries, and 1/5 on rent, a man has \$120 ...
The difference of the squares of two positive consecutive odd integers
the difference of the squares of two positive consecutive odd integers is 32...
Find two consecutive odd integers
Find two consecutive odd integers such that the square of the larger is 3 less than 12 times the smaller
What is the square root of 48 minus the square root of 75?
The product of two consecutive odd numbers
The product of two consecutive odd numbers is 195...
If k is an interger
If k is an interger and 0.0010101 x 10k is greater than 1...
The sum of the reciprocals of two consecutive odd integers
The sum of the reciprocals of two consecutive odd integers is 8/15 ...
The square of the largest of three consecutive integers
The square of the largest of three consecutive integers is 320 less than the sum of the squares of the two smaller ...
One person says that numbers in radicals
One person says that numbers in radicals are useless because they do not have any real world relevance. Give a convincing practical example to show this person that they are very practical and we need ...
Farmer Joe has some chickens
Farmer Joe has some chickens. 1/3 of the chickens are roosters. 3/5 of the remaining were hens. There were 30 ...
If you receive a pay increase
If you receive a pay increase of 12% what is your new pay rate, assuming your old one was \$14...
What is the square root
What is the square root of 49 multiplied by the square root of 9?
How many yards of material
How many yards of material from a 24-yard length of cloth remain after 3 pieces, each 3 1/2 yards long and 5 pieces, each 2 1/4 yards ...
Jon bought groceries
Jon bought groceries for \$105.30 and paper product for \$35.50. The total bill including tax was \$142.93. There was no tax charged on the ...
A picture frame is 20cm by 14cm
A picture frame is 20cm by 14cm.  the picture, inside the frame, takes up 160cm2...
7 times the reciprocal of a number
7 times the reciprocal of a number plus 2/3 is 3...
Mrs. Wee bought 5 trays of eggs
Mrs. Wee bought 5 trays of eggs. Each tray contained 30 eggs.  On her way home she fell and broke 2/5 of the eggs.  She used 5/9 of the remaining ...
One integer is 2 more than 5 times
One integer is 2 more than 5 times another integer. If the difference of the 2 integers is 26...
Four friends share a pizza
Four friends share a pizza. Maria ate one-third ,Ally and Mindy each ate one-frourth of the pizza and Bethany ate one-sixth.
A. into how many equal slices did they need to cut the pizza?
...
Sabrina and Samantha worked on weekends
Sabrina and Samantha worked on weekends and holidays. They were paid by the day, not the hour. Each of them earned the same whole number of dollars. Last month Sabrina earned \$184 and Samantha earned \$207...
The high yesterday was 32 and the low was -12
The high yesterday was 32 and the low was -12. What was the difference in the temperatures?_________
One-fifth of Ed`s Auto sales last year
One-fifth of Ed's Auto sales last year were new customers. If 600 cars were sold to new ...
Lyle is putting his videotapes on a shelf
Lyle is putting his videotapes on a shelf. The shelf is 12 inches long. If each videotape is 1 1/2 inches ...
The temperature on Monday
The temperature on Monday was 13 and on Tuesday was -5.  What was the difference in the temperatures?_________
Tom had 15 trucks. He gave 2/5 of them to his ...
The product of two consecutive integers
The product of two consecutive integers is 12 more than the square of the smaller ...
1 out of 7 students failed an exam
1 out of 7 students failed an ...
integersThe sum of three consecutive odd integers
The sum of three consecutive odd integers is 57...
If you are laying out a photo page
If you are laying out a photo page and have each photo cut to 3 2/5 inches ...
The sum of two complex numbers
The sum of two complex numbers is 4 and their product is 13...
At a little league football game
At a little league football game, the concession stand sold 6 orange sodas for every 5 grape sodas sold. If 255 sodas were ...
Find 4 consecutive even integers
Find 4 consecutive even integers where the product of the two smaller numbers is 56 less that the product of the two larger numbers.
A motor boat can travel
A motor boat can travel 20 mph in still water. If the boat can travel 3 miles down stream on a river in the same time it takes to travel 2 miles ...
A new car loses 20% of it`s original value
A new car loses 20% of it's original value when you buy it and 8% every year after. If a new car is valued \$20,000 and is now worth \$9,600...
Ariana took 2 hours longer to drive 360 miles
Ariana took 2 hours longer to drive 360 miles on the first day of a trip thans she took to drive 270 miles on the second ...
The temperature in Dallas was 20
The temperature in Dallas was 20 and in Chicago the temperature was -10. What was the difference in the temperatures?_________
The sum of two integers
The sum of two integers is -3. When the greater integer is subtracted from the lesser integer, the difference is -11...
Find a number such that the sum of three times the number
Find a number such that the sum of three times the number and 25 times the reciprocal of the number is 20
rational numbers
The sum of a number and its reciprocal is 29/10...
There are 42 pupils in a class
There are 42 pupils in a class. 3/4 of the boys and 2/3 of the girls travel to school by bus. The total number of boys and girls who travel to school by bus is 30. How many boys are there in the ...
The sum of two rational numbers
The sum of two rational numbers is 15/16. If one of them is 121/112...
Suppose you buy 1 2/3 lb of bananas
Suppose you buy 1 2/3 lb of bananas for .65 ...
Ty ran 23 5/6 miles
Ty ran 23 5/6 miles. Tubba Bubbu ran 7 times more far than ...
Lala bought 36 oranges
Lala bought 36 ...
percents
Jill created a metal containing 47% silver by combining two other metals.  One of these other metals weighed 4 lb. and contained 57% silver.  If the other weighed 8 ...
Monica went to store and buy
Monica went to store and buy 3 chocalate milk for 2.99 all ...
rational numbers
Is 3pi/2  a rational ...
percents
Scott made a nut mixture that contains 67% peanuts by mixing together 10 oz. of mixed nuts that contain 64% peanuts and 5 oz. of a different brand of mixed ...
If a single 2 hp motor draws
If a single 2 hp motor draws 13.8 amps current on 115 volt AC ...
The sum of a number and 8 times its reciprocal
The sum of a number and 8 times its reciprocal is 6...
Jim uses 1/3 of his land
Jim uses 1/3 of his land for growing durians. 3/8 for guavas. 1/4 for bananas and remaining 9 hectres for ...
Nine times the reciprocal of a number
Nine times the reciprocal of a number equals 3 times the reciprocal of 7...
The sum of two numbers
The sum of two numbers is 12. The sum of the squares of these two numbers is 74...
Sum of 2 consecutive even integers
Sum of 2 consecutive even integers is at most 400. Find the pair of intergers
Roma`s skates cost
Roma's skates cost \$175. Every 2 weeks that she skates, she spends \$4.50 on sharpening the blades. One year, she spent a total of \$256 on the cost of skates and ...
There was 20 liters of milk at the refrigerator
There was 20 liters of milk at the refrigerator this morning. Jenny drank 7 5/6 liters of it. Along came Olivia who drank 1 2/5 liters of the milk. Then Sarah woke up and drank 3 2/8 of ...
Pepe counted 57 half gallons of orange juice
Pepe counted 57 half gallons of orange juice in his ...
The width of a rectangle
The width of a rectangle is 16 feet less than 3 times the length. If the area is 35 square ...
A chemist wishes to strengthen a mixture
A chemist wishes to strengthen a mixture that is 10% alcohol to one that is 30% ...
The product of two consecutive odd integers
The product of two consecutive odd integers is 195...
Red Lobster had 300 lobsters ready for yesterday's service. They have sold 32 percent of ...
You want to shoot and make 25 shots
You want to shoot and make 25 shots per day. If you shoot in sets of ten and make 50%. how many sets will it take to make 25 shots
One-third of the principal square root
One-third of the principal square root of a number is 5...
Use the formula d=4.9t2 for the distance d in meters an object will fall in t seconds. An object is dropped from an airplane 1,240 meters over the ...
Phillipe works for a computer store
Phillipe works for a computer store that pays a 12% commisssion and no ...
Pepe counted 57 half-gallons of orange juice
Pepe counted 57 half-gallons of orange juice in his ...
A pay check lists the gross pay
A pay check lists the gross pay as \$1208.34 and the net pay \$900.21...
You belong to a wholesale buying club
You belong to a wholesale buying club. You can order items from the club with a markup of 8% over the wholesale price. A local retail store, which gets its merchandise at the same wholesale price, offers to sell you those same items at 10% off the shelf ...
Jim cut down 500 trees this year
Jim, the lumberjack, cut down 500 trees this year. This is a 25% increase from the number of trees that he cut down last ...
If x is 250% of y
If x is 250% of ...
The new amount is \$66
The new amount is \$66. This is 10% increase over the old ...
You get on a diet to lose excess weight
You get on a diet to lose excess weight of 80 pounds. You lost 25 percent of the excess. The following month, you take a vacation and increase your excess weight by 20 percent. You get on a diet again  and lose 25 percent of the excess ...
There are shirts in a box
There are shirts in a box. 1/2 of them are small. 2/5 of them are medium. and 5 of them are ...