Lesson Worksheet: Applications on Systems of Linear Equations Mathematics • 8th Grade

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

Q1:

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

Q2:

A man’s age is 4 times his son’s age. In 5 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

Q3:

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

Q4:

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?

Q5:

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

Q6:

A 30 ft 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?

Q7:

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

Q8:

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

Q9:

Anthony buys 5 apples and 3 bananas from a grocery store and pays $3.40. Hannah 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¢.

Q10:

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.

Q11:

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

Q12:

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?

Q13:

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

Q14:

Jennifer’s grandad has been collecting 2p and 5p coins. She has 163 coins in total and their value is £5.87. How many 5p coins does she have?

Q15:

Given that there are two supplementary angles and that the measure of seven times the smaller angle is equal to twice the measure of the bigger one, determine the measure of both angles.

  • A70, 110
  • B140, 70
  • C40, 110
  • D140, 40

Q16:

When the digits of a two digit number are reversed, the result is 27 more than the original number. If the sum of the digits is 9, what was the original two digit number?

Q17:

In a school competition, students score points for completing long and short puzzles. No points are awarded for incomplete puzzles. James scored 85 points for completing 4 long and 5 short puzzles, and Matthew scored 85 points for completing 3 long and 8 short puzzles. How many points did Ethan score for completing 5 long and 5 short puzzles?

Q18:

Some girls and boys attend a club. Six times the number of girls at the club is 33 more than the number of boys, and 3 times the number of girls is 33 less than six times the number of boys. How many girls and how many boys attend the club?

  • Anumber of girls =7, number of boys =26
  • Bnumber of girls =7, number of boys =5
  • Cnumber of girls =7, number of boys =9
  • Dnumber of girls =5, number of boys =27

Q19:

A total of 20 LE is made from 25-piastre and 50-piastre banknotes. If there are 44 banknotes altogether, how many are there of each type?

  • A8 of 50 piastres, 36 of 25 piastres
  • B156 of 50 piastres, 136 of 25 piastres
  • C36 of 50 piastres, 8 of 25 piastres
  • D136 of 50 piastres, 156 of 25 piastres

Q20:

The cost of 3 pens and 5 books is 38 LE. The cost of 5 pens and 2 books is 19 LE. Find the cost of a book and the cost of a pen.

  • Aa book = 11 LE, a pen = 3 LE
  • Ba book = 7 LE, a pen = 3 LE
  • Ca book = 7 LE, a pen = 1 LE
  • Da book = 1 LE, a pen = 3 LE
  • Ea book = 1 LE, a pen = 11 LE

Q21:

The sum of two numbers is 56. Given that one of the numbers is one seventh of the other, what are the two numbers?

  • A7, 42
  • B8, 56
  • C17, 39
  • D8, 42
  • E7, 49

Q22:

Find two numbers with a sum of 42 where one number is one-fifth of the other.

  • A8, 42
  • B7, 35
  • C21, 105
  • D14, 70
  • E10, 52

Q23:

The length of a rectangle is 6 cm more than its width. If its perimeter is 52 cm, what are its dimensions?

  • A20 cm, 10 cm
  • B32 cm, 13 cm
  • C16 cm, 10 cm
  • D16 cm, 22 cm

Q24:

A family are playing on a seesaw at the park. The seesaw is balanced when the father and daughter sit at one end and two brothers sit at the other. The father’s weight is 7 times his daughter’s and the sons have a combined weight of 96 kg. How much does the daughter weigh?

Q25:

A man’s age was four times his daughter’s age, 4 years ago. In 5 years, his age will be three times his daughter’s. Find their ages now.

  • A8 years, 72 years
  • B22 years, 72 years
  • C8 years, 76 years
  • D22 years, 76 years

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