# System Word Problems

Many students find systems word problems difficult. At TuLyn, we created word problems on systems to help you better understand systems.

### Systems Of Equations Word Problems

Practice systems of equations word problems.

### Dependent System Word Problems

Practice dependent system word problems.

### Inconsistent Systems Word Problems

Practice inconsistent systems word problems.

### Nonlinear Systems Word Problems

Practice nonlinear systems word problems.

### Linear Systems Word Problems

Practice linear systems word problems.

# Submit your word problem on systems:

Are you looking for systems word problems? TuLyn is the right place. We have tens of word problems on systems and hundreds on other math topics.

Below is the list of all word problems we have on systems.

# Systems Word Problems

• 9 times the side of one square exceeds (#3248)
9 times the side of one square exceeds the perimeter of the second square by 1 metre and 6 times the area of the second square exceeds 29 times the area of the first by 1 square ...
solving systems of equations, systems of equations, solving equations, systems, equations
• A bike shop rents mountain bikes (#3256)
A bike shop rents mountain bikes for a \$8.50 insurance charge plus \$3.50 per hour. For how many hours can a person rent a bike with \$32...
systems of linear equations, systems of equations, linear equations, systems, equations
• A boat traveled 126 miles (#86)
A boat traveled 126 miles downstream and back.  The trip downstream took 6 hours.  The trip back took 42 ...
systems of equations, systems, equations
• A boy walked at the rate (#1775)
A boy walked at the rate of 2mph and then rode a bicycle back the same distance at the rate of 10mph. If the entire trip took 3 ...
systems of equations, systems, equations
• A bulldozer can move 25 tons/h of material (#2440)
A bulldozer can move 25 tons/h of material,and an end loader can move 18 tons/h.The bulldozer costs \$75/h to operate,and the end loader costs \$%0/h to operate.During a 1 hour construction company moved 204 tons at a cost of \$600...
systems of linear equations, systems of equations, linear equations, systems, equations
• A candy shop sells two new flavors of candy (#2471)
A candy shop sells two new flavors of candy. Chewy nut and chocolate chew. Each barrel of chewy nut requires 8 pounds of nuts and 4 pounds chocolate and has a profit of \$540. Each barrel of chocolate chew requires 8 pounds of nuts and 2 pounds of chocolate and has a profit of \$210. There are 64 pounds of nuts and 32 pounds of chocolate in stock, and the owner does not want to buy more stock to make the ...
systems of equations, systems, equations
• A car leaves New York traveling south (#3115)
A car leaves New York traveling south at 50 m/hr. One hour later, another car leaves New York on the same road traveling south at 55m/...
systems of equations, systems, equations
• A chemical plant is rectangular and has a length (#1721)
A chemical plant is rectangular and has a length of a hundred meters and a width of sixty meters. A safety zone of uniform width surrounds the plant. if the area of the safety zone equals the area of the ...
solving systems of equations, systems of equations, solving equations, systems, equations
• A child has \$14.35 worth of nickels (#1301)
A child has \$14.35 worth of nickels and dimes in her piggy bank. there is a total of 165 ...
systems
• A community center sells (#1806)
A community center sells a total of \$301 tickets for a basketball game. An adult ticket costs \$3. A student ticket costs \$1. The sponsors collect \$487 in ticket ...
systems of equations, systems, equations
• A company borrowed 600,000 for one year (#2375)
A company borrowed 600,000 for one year. Part was at 8% interest, part was at 10% interest rate. How much at each rate if annual interest is \$53...
systems of equations, solving systems of equations, systems, equations, solving equations
• A farmer raises wheat and soybeans (#2536)
A farmer raises wheat and soybeans on 215 acres. if he wants to plant 31 more acres in wheat than ...
systems of equations, systems, equations
• A grocer plans to mix candy (#809)
A grocer plans to mix candy that sells for \$2 a pound with candy that sells for \$4 a pound to get a mixture that sells for \$2.75 a ...
systems of equations, systems, equations
• A mixture of 12 liters of chemical A (#2030)
A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C
is required to kill a certain destructive crop insect. Commercial spray X contains 1, 2, and 2
parts, respectively, of these chemicals. Commercial spray Y contains only chemical C.
Commercial spray Z contains only chemicals A and B in equal ...
equations, systems of equations, systems
• A motorboat travels 332 in 4 hours (#2571)
A motorboat travels 332 in 4 hours going upstream 555 and in 5 hours going downstream. What is the speed of the boat in still ...
systems of linear equations, systems of equations, linear equations, systems, equations
• A motorcycle breaks down and the rider (#1171)
A motorcycle breaks down and the rider has to walk the rest of the way to work. The motorcycle was traveling at 45 mi/hr, and the rider walks at a speed of 6 mi/hr. The distance from home to work is 25 miles, and the total time of the trip was 2 ...
equations, systems, systems of equations
• A rectangle`s width is 4 times the length (#3542)
A rectangle's width is 4 times the length. The perimeter is 30 ...
solving systems of equations, systems of equations, solving equations, systems, equations
• A rectangular garden is 5 feet longer (#3477)
A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square ...
systems, solving systems of equations, systems of equations, polynomials, solving equations, equations
• A rectangular lot whose perimeter (#2249)
A rectangular lot whose perimeter is 360 ft. is fenced along 3 sides. An expensive fencing along the lot's length costs \$20 per ft. and an inexpensive fencing along the 2 side widths costs \$8 per ft. The total cost of the fencing along the 3 sides comes to \$3280...
systems of linear equations, systems of equations, linear equations, systems, equations
• A rectangular patio is 7 ft longer (#1448)
A rectangular patio is 7 ft longer than it is ...
solving systems of equations, systems of equations, solving equations, systems, equations
• A soccer team bought ice cream cones (#1990)
A soccer team bought ice cream cones to celebrate a victory. The total cost of 12 double cones and 8
single cones was \$17. A double cone cost \$0.25 more than a single ...
linear systems, systems
• A total of \$8000 is invested in two funds (#1134)
A total of \$8000 is invested in two funds paying 4% and 5% annual interest. The combined annual interest is \$350...
systems of equations, systems, equations
• A total of 512 tickets were sold (#3120)
A total of 512 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets ...
systems of equations, systems, equations
• Alvin is 15 years older than Elga (#3370)
Alvin is 15 years older than Elga. The sum of their ages is 85...
equations, solving systems of equations, systems of equations, solving equations, systems
• Amy took a test that had a math section (#2229)
Amy took a test that had a math section and an English section. She earned a total score of 88. Her math score was 6 points higher than her English ...
systems of equations, systems, equations
• Andres and Biloy working together (#921)
Andres and Biloy, working together, can build a chicken house in 6 2/3 hours. Andres became ill after 3 hours of working with Biloy, and Biloy finished the job, continuing to work alone in 8 1/4 more ...
solving systems of equations, systems of equations, solving equations, systems, equations, work rate, rate
• April buys eight books (#197)
April buys eight books for \$44. Paperback books cost \$4 and hardback cost \$8...
systems, equations, systems of equations
• Aprroximately 4.5 million wrecked cars (#233)
Aprroximately 4.5 million wrecked cars are recycled in two consecutive years. There were 700,000 more recycled the second year than the first ...
solving equations, equations, systems of equations, systems, solving systems of equations
• At an IMAX theatre, the giant rectangular screen (#3321)
At an IMAX theatre, the giant rectangular screen has a width 36 feet less than its length. If the perimeter of the screen is 332 ...
systems of equations, systems, equations
• At full speed, an airplane can travel (#1815)
At full speed, an airplane can travel 4500 miles with the wind in 6 hours, but it requires 10 hours to travel the same distance against the wind.
what is the wind ...
systems of equations, systems, equations
• At the afternoon matinee movie (#1982)
At the afternoon matinee movie 3 adult tickets and 4 child tickets cost \$41, and 4 adult tickets and 3 child tickets cost \$43...
linear equations, equations, systems of equations, systems, systems of linear equations
• copper that was 63% pure (#1100)
copper that was 63% pure was melted together with copper that was 90% pure to make 18 kilograms of an alloy that was 75% ...
equations, systems, systems of equations
• Dave sold popcorn and pretzels (#1057)
Dave sold popcorn and pretzels at the game. He sold a told of \$336 worth of both. He sold popcorn for \$2.50 and pretzels for \$2 each.  He sold twice as many bags of popcorn than ...
systems, systems of equations, equations
• During a used book sale (#871)
During a used book sale, a total of 62 books were sold and \$103 was made. The books were priced at \$1.50 or \$2.00 each. Find how many books are sold at \$1.50 and how many at \$2.00
systems of equations, systems, equations
• Find a two-digit number (#1353)
Find a two-digit number where the sum of the digits is 6 and the number is 6 times the unit's digit.
systems of equations, systems, equations
• Find the value of two numbers (#2965)
Find the value of two numbers if their sum is 12 and their difference is 4
systems of equations, systems, equations
• I have \$50 consisting of all \$5 bills and \$1 bills (#3184)
I have \$50 consisting of all \$5 bills and \$1 bills and total of 22 ...
systems of equations, systems, equations
• If 3 times the second number (#2018)
If 3 times the second number is subtracted from the sum of the first number and 3 times the third ...
systems of equations, systems, equations
• If jennifer were three times as old (#3009)
If Jennifer were three times as old as she was five years ago, she will be twenty seven more than current ...
systems of equations, systems, equations
• If the price of 3 hats and 7 shirts (#2047)
If the price of 3 hats and 7 shirts is \$189 and 5 hats and 11 shirts is \$301...
equations, systems, systems of equations
• Juan goes to a bank and gets change (#1061)
Juan goes to a bank and gets change for a \$50 bill consisting of all \$5 and \$1 bills. There are 22 bills in ...
equations, systems, systems of equations
• Jurassic Park charges \$20 for adults (#3468)
Jurassic Park charges \$20 for adults and \$12 for children. Total bill for 454 people was \$3860...
systems, polynomials, solving systems of equations, systems of equations, solving equations, equations
• Marco and Celeste ride bikes (#3191)
Marco and Celeste ride bikes. Marco rides 10 mph and Celeste rides 12 ...
linear systems, systems
• Mark bought 114 meters of fencing (#3288)
Mark bought 114 meters of fencing to enclose an area of pasture for his sheep. He plans to use all of the fencing to make a rectangle that is twice as long as it is ...
solving systems of linear equations, systems of linear equations, systems of equations, linear equations, systems, equations
• Mike bought 3 cokes and 2 fries (#2307)
Mike bought 3 cokes and 2 fries and paid 5.25. he also noticed the cost of an order of fries is 2 times the cost of a ...
systems of equations, systems, equations
• One positive integer is 8 less (#816)
One positive integer is 8 less than twice another and the sum of their squares is 244
equations, systems of equations, solving quadratic equations, solving systems of equations, quadratic equations, solving equations, systems
• Paul bought 8 eating utensils (#2057)
Paul bought 8 eating utensils for a total of \$26. Spoons cost \$4 and forks cost \$3...
systems of equations, systems, equations
• Ruby is 6 years younger than Carlo (#3274)
Ruby is 6 years younger than Carlo. The average of their ages now, is twice Ruby's age 5 years ...
solving systems of equations, systems of equations, solving equations, systems, equations
• Rudy must play 12 commercials (#3521)
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...
equations, solving systems of equations, systems of equations, solving equations, systems
• Shoes cost \$20 per pair and boots cost \$60 per pair (#1722)
Shoes cost \$20 per pair and boots cost \$60 per pair. Arlene and Jerry spent \$8000 and bought 3 times as many boots as ...
systems of equations, systems, equations
• Simone has 16 player on her soccer team (#121)
Simone has 16 player on her soccer team. There are 6 more boys than ...
systems of equations, solving systems of equations, systems, equations, solving equations
• systems of equations (#87)
The school that Asanji goes to is selling tickets to a play.  On the first day of ticket sales the school sold 10 senior citizen tickets and 9 student tickets for a total of \$200.  The school took in \$87 on the second day by selling 7 senior citizen tickets and 1 student ...
systems of equations, systems, equations
• Systems Of EquationsThe sum of three consecutive numbers (#1640)
The sum of three consecutive numbers is the same as twice the value of the last ...
equations, systems, systems of equations
• Tasty Bakery sells three kinds of muffins (#2235)
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 25 cents each, oatmeal muffins at 30 cents each, and cranberry muffins at 35 cents each. Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins. If he spends \$4.70 on 15 ...
systems of equations, systems, equations
• The area of a triangle (#3232)
The area of a triangle is 30in2. The base of the triangle measures 2 in. more than twice the height of the ...
systems of equations, solving systems of equations, triangles, polygons, shapes, plane figures, curves, solving equations, systems, equations
• The band boosters are organizing a trip (#2976)
The band boosters are organizing a trip to a national competion for the 226-member marching band. A bus will hold 70 students and their instruments. A van will hold 8 students and their instuments. A bus costs \$280 to rent for the trip. A van costs \$70 to rent for the trip. The boosters have \$980 to use for ...
solving systems of linear equations, systems of linear equations, systems of equations, linear equations, systems, equations
• The board of directors of a corporation (#3364)
The board of directors of a corporation grant a bonus of \$5000 to be divided between two employees. The senior employee receives \$1200 more than the junior ...
linear equations, systems of equations, systems of linear equations, solving systems of linear equations, systems, equations
• The chief executive has just requested (#2911)
The chief executive has just requested that Suzie's division make 300 gallons of sparkling water to sell at \$6 per gallon. She wishes to mix 3 grades of water selling for \$9, \$3, \$4.50. She must use twice as much of the 4.50 water as the 3.00...
systems of equations, systems, equations
• The formula represents the number of households (#2278)
The formula N=4x2+5x+1 represents the number of households N, in thousands, in a certain city that have a computer x years after 1990. According to the ...
systems of equations, systems, equations
• The hypotenuse of a right triangle (#2792)
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the
remaining ...
right triangles, triangles, polygons, shapes, plane figures, curves, solving systems of equations, solving equations, systems of equations, equations, systems
• The length of a certain rectangle (#3290)
The length, L, of a certain rectangle is four feet more than three times its width, W. The perimeter of the rectangle is 88 ...
solving systems of equations, rectangles, perimeter, shapes, plane figures, systems of equations, solving equations, systems, equations
• The length of a rectangle is 2 feet more (#1401)
The length of a rectangle is 2 feet more than twice the width. The perimeter of the rectangle is 40 square feet. Find the length and width of the rectangle. (Hint: First write the length using an algebraic expression that contains width)
solving equations, systems of equations, solving systems of equations, systems, equations
• The length of a rectangular field (#3277)
The length of a rectangular field is 24 meters. This is 3 meters less than twice the ...
systems of equations, systems, equations
• The perimeter of a court is 108 meters (#3526)
The perimeter of a court is 108 meters.  If the length is 6 meters longers than twice the ...
equations, systems of equations, systems, solving equations, solving systems of equations
• The perimeter of a rectangular (#3046)
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2...
perimeter, shapes, solving equations, systems of equations, equations, systems, solving systems of equations
• The side of a square house is 24 ft long (#1913)
The side of a square house is 24 ft long, and the house is located on a lot which is 50 ft longer than it is wide. The perimeter of the lot is 20 ft more than 5 times the perimeter of the ...
solving systems of equations, systems of equations, solving equations, equations, systems
• The sum of the digits of a two-digit number (#891)
The sum of the digits of a two-digit number is 13. The number is 27 more than the number formed by interchanging the tens digit with the one ...
systems of equations, systems, equations
• The sum of the squares (#928)
The sum of the squares of two consecutive positive numbers is 61...
systems of equations, consecutive integers, solving equations, solving systems of equations, equations, systems, integers, number sense, numbers
• The sum of the squares of the two (#1053)
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 ...
polynomials, consecutive integers, solving systems of equations, systems of equations, solving equations, systems, equations, integers, number sense, numbers
• The sum of the squares of two consecutive (#1895)
The sum of the squares of two consecutive negative even integers is 100...
greatest common factor, solving equations, equations, systems, systems of equations, solving systems of equations
• The sum of the squares of two consecutive positive even integers (#2056)
The sum of the squares of two consecutive positive even integers is 244...
systems of equations, systems, equations
• The sum of three numbers (#3074)
The sum of three numbers is 15. The third number is nine less than the sum of the first and second number. The first number is four more than the third ...
systems of equations, systems, equations
• The sum of two numbers (#1176)
The sum of two numbers is 20. Their difference is 4...
systems, systems of equations, equations
• The total proceeds from a used book sale (#3528)
The total proceeds from a used book sale were \$115. A total of 65 books were sold. The books were priced at \$1.50 and \$2.00 each. How many books were sold for \$1...
systems, solving systems of equations, systems of equations, equations, solving equations
• There are 48 heads and 134 legs (#1943)
There are 48 heads and 134 legs among the chicken and pigs on the ...
systems of equations, systems, equations
• There are a total of 126 cats and dogs (#2691)
There are a total of 126 cats and dogs at an animal shelter. For every 5 dogs, there are 4 ...
solving equations, systems, systems of equations, equations, solving systems of equations
• There is a bag that contains (#1394)
There is a bag that contains: blue, green, and red marbles. There is a total value of 10 marbles. There are twice as many blue marbles as there are green, and the amount of red is one more than three times the amount of ...
equations, systems, systems of equations
• Three consecutive even integers (#1447)
Three consecutive even integers are such that the square of the third is 100 more than the square of the ...
consecutive numbers, consecutive integers, solving systems of equations, systems of equations, solving equations, systems, equations, integers, number sense, numbers
• Tickets for a school play cost (#1747)
Tickets for a school play cost \$4 for adults and \$2 for students. At the end of the play, the school sold a total of 105 tickets and collected \$360. Write a linear system. Let x be the number of adult tickets sold and let y be the number of student tickets sold. Graph the ...
equations, systems, systems of equations
• Tickets to a movie cost (#1165)
Tickets to a movie cost \$7.25 for adults and \$5.50 for students. A group of friends purchased 8 tickets for \$52.75...
solving equations, solving systems of equations, systems, systems of equations, equations
• Traci and Gene walk at the same rate (#2145)
Traci and Gene walk at the same rate and jog at the same rate.Traci walks for 1 hour and jogs for 1 hour, and covers a distance of 17km. Gene walks for 2 hours and jogs for half and hour, and covers a distance of 16...
systems of equations, systems, equations
• Two houses are for sale on the same street (#3503)
Two houses are for sale on the same street. The second house has 1000 square feet less than twice the square feet of the first house. Together the houseshave 4400 square ...
solving systems of equations, systems of equations, solving equations, systems, equations
• Two rental airplanes were flown (#2169)
Two rental airplanes were flown a total of 54 hours in one month. One plane rents for \$105/h, and the other rents for \$130/h. The total income from the two planes was \$6570...
systems of equations, systems, equations, solving systems of equations, solving equations
• You are selling tickets to a high school play (#2760)
You are selling tickets to a high school play. Student tickets cost \$5 and general admission tickets cost \$8. you sell 566 tickets and collect \$3797...
solving equations, equations, solving systems of equations, systems of equations, systems