Worksheet: Applications on Systems of Linear Equations

In this worksheet, we will practice translating a real-life problem into a system of equations and finding its solution(s).


Two cousins were born 8 years apart. How old will the elder be when the sum of their ages is equal to 20 years?


A man’s age is 4 times his son’s age. In five years, the sum of their ages will be 105. How old are they now?

  • A19 years, 76 years
  • B25 years, 43 years
  • C21 years, 84 years
  • D23 years, 60 years
  • E20 years, 62 years


I am thinking of two numbers. Use the clues to determine what the numbers are.

  • The product of the two numbers is 48.
  • The difference between the two numbers is 2.
  • A6 and 4
  • B5 and 3
  • C7 and 5
  • D9 and 7
  • E8 and 6


In a test with 20 questions, 𝑥 marks are awarded for each correct answer and 𝑦 marks are deducted for each incorrect answer. Liam answered 12 questions correctly and 8 questions incorrectly, and he scored 44 points. Amelia answered 14 questions correctly and 6 questions incorrectly, and she scored 58 points. How many points were deducted for each incorrect answer?


Michael bought 3 muffins and 2 cookies for $3.30, while James bought 2 muffins and 5 cookies for $5.50. Work out the price of a single muffin and a single cookie.

  • Amuffin: $0.60, cookie: $0.75
  • Bmuffin: $0.90, cookie: $0.50
  • Cmuffin: $0.50, cookie: $0.75
  • Dmuffin: $0.75, cookie: $0.90
  • Emuffin: $0.50, cookie: $0.90


A 30-foot-long ribbon was cut into three pieces. The first piece is one-third as long as the second piece, and the third piece is 4 feet longer than three times the length of the second piece. How long is the longest ribbon piece?


A store clerk sold 60 pairs of sneakers. The high-tops sold for $98.99 and the low-tops sold for $129.99. If the receipts for the two types of sales totaled $6,404.40, how many of each type of sneaker were sold?

  • Ahigh-tops: 45 pairs, low-tops: 15 pairs
  • Bhigh-tops: 15 pairs, low-tops: 45 pairs
  • Chigh-tops: 40 pairs, low-tops: 20 pairs
  • Dhigh-tops: 30 pairs, low-tops: 30 pairs


A sorority held a bake sale to raise money and sold brownies and chocolate chip cookies. They priced the brownies at $1 and the chocolate chip cookies at $0.75. They raised $700 and sold 850 items. How many brownies and how many cookies were sold?

  • Abrownies: 250, chocolate chip cookies: 600
  • Bbrownies: 300, chocolate chip cookies: 550
  • Cbrownies: 350, chocolate chip cookies: 500
  • Dbrownies: 200, chocolate chip cookies: 650


I am thinking of two numbers. Use the clues to determine what the numbers are.

  • When you divide one by the other, the quotient is 8.
  • The sum of the two numbers is 81.
  • A72 and 9
  • B70 and 11
  • C4 and 8
  • D75 and 6
  • E71 and 10


A chemistry teacher needs to mix a 30% salt solution with a 70% salt solution to make 20 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?

  • A8 qt of the 30% solution, 12 qt of the 70% solution
  • B10 qt of the 30% solution, 10 qt of the 70% solution
  • C15 qt of the 30% solution, 5 qt of the 70% solution
  • D12 qt of the 30% solution, 8 qt of the 70% solution
  • E5 qt of the 30% solution, 15 qt of the 70% solution


Jacob has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest and part at 12% interest. How much does Jacob need to invest in each option to get a total 11% return on his $20,000?

  • A$410,000 at 8%, $10,000 at 12%
  • B$15,000 at 8%, $5,000 at 12%
  • C$18,000 at 8%, $2,000 at 12%
  • D$5,000 at 8%, $15,000 at 12%
  • E$2,000 at 8%, $18,000 at 12%


Hannah starts riding her bike at 20 mph. After a while, she slows down to 12 mph and maintains that speed for the rest of the trip. The whole trip of 70 mi takes her 4.5 h. For what distance did she travel at 20 mph?


A rectangle’s length is 16 cm less than four times its width. Given that its perimeter is equal to that of a square of side 12 cm, find the dimensions of the rectangle.

  • A3 cm, 22 cm
  • B4 cm, 8 cm
  • C8 cm, 16 cm
  • D3 cm, 13 cm


Noah buys 5 apples and 3 bananas from a grocery store and pays $3.40. Madison buys 3 apples and 2 bananas from the same store and pays $2.10. Work out the price of a single apple and a single banana.

  • AAn apple is 25¢ and a banana is 15¢.
  • BAn apple is 45¢ and a banana is 35¢.
  • CAn apple is 26¢ and a banana is 14¢.
  • DAn apple is 50¢ and a banana is 30¢.
  • EAn apple is 47¢ and a banana is 6¢.


William buys 4 burgers and 3 hot dogs for $16 from a fast-food vendor. Matthew buys 3 burgers and 4 hot dogs for $15.50 from the same vendor. Work out the price of a single burger and a single hot dog.

  • AA burger is $4.42 and a hot dog is $0.56.
  • BA burger is $2.50 and a hot dog is $2.
  • CA burger is $2 and a hot dog is $2.50.
  • DA burger is $3 and a hot dog is $2.50.
  • EA burger is $0.56 and a hot dog is $4.42.


A bank offers two savings account options. In the first one, a deposit of $40 is received every year for an initial capital of $1,000. In the second option, an annual interest rate of 2.8% is offered and it’s compounded monthly. Which option is more profitable after 30 years?

  • AOption 1
  • BOption 2


A library decides to put in place a new fine system as a stronger incentive for borrowers to return items on time. Instead of issuing a fine of 20¢ per day and per item, the fine is 20¢ for 1 day after the return date, 40¢ for 2 days, 80¢ for 3 days, and so on. How much more will a borrower pay for an item returned 7 days after the return date?


A concert venue sells single tickets for $40 each and couple tickets for $65. If the total revenue was $18,090 and 321 tickets were sold, how many of each type of ticket did they sell?

  • A100 single tickets, 221 couple tickets
  • B210 single tickets, 111 couple tickets
  • C121 single tickets, 200 couple tickets
  • D111 single tickets, 210 couple tickets


Two planes flying in opposite directions pass each other. One is flying at 450 mph and the other at 550 mph. How long will it take before they are 4,000 miles apart?


Sophia invested 1.1 million dollars in two land investments. Her return on the first investment, Swan Peak, was a 110% increase on the money she had invested. On her second investment, Riverside Community, she earned 50% over what she had invested. Given that she earned $1 million in profit, how much did she invest in each of the land deals?

  • ASwan Peak: $650 000, Riverside: $350 000
  • BSwan Peak: $750 000, Riverside: $350 000
  • CSwan Peak: $750 000, Riverside: $250 000
  • DSwan Peak: $350 000, Riverside: $750 000


A concert manager counted 350 ticket receipts the day after a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $5,075 were taken in. How many student tickets and adult tickets were sold?

  • Astudent tickets: 250, adult tickets: 100
  • Bstudent tickets: 300, adult tickets: 50
  • Cstudent tickets: 200, adult tickets: 150
  • Dstudent tickets: 150, adult tickets: 200


A Jeep and a BMW entered a highway at the same interchange, heading in opposite directions. The Jeep entered the highway 30 minutes before the BMW and traveled 7 mph slower than the BMW. Two hours after the BMW entered the highway, the two cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.

  • AThe Jeep: 72 mph, the BMW: 65 mph
  • BThe Jeep: 65 mph, the BMW: 72 mph
  • CThe Jeep: 57 mph, the BMW: 61 mph
  • DThe Jeep: 72 mph, the BMW: 80 mph


The difference between the measures of the acute angles in a right triangle is 52. Find the measure of each acute angle.

  • A38, 52
  • B19, 52
  • C64, 26
  • D38, 71
  • E19, 71


Last year, 276 students enrolled in a freshman-level chemistry class. At the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number of students who failed the class.

  • APassed: 230, failed: 46
  • BPassed: 200, failed: 76
  • CPassed: 46, failed: 230
  • DPassed: 236, failed: 40


In a garden, there are green and red tomatoes. The red tomato weighs 10 oz, and the green 4 oz. Overall, there are 30 tomatoes with a combined weight of 13 lb. How many of each type of tomato are there?

  • A20 green tomatoes, 10 red tomatoes
  • B17 green tomatoes, 13 red tomatoes
  • C13 green tomatoes, 17 red tomatoes
  • D15 green tomatoes, 15 red tomatoes

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