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Lesson: Using Systems of Equations to Solve Real-Life Problems

In this lesson, we will learn how to translate a real-life problem into a system of equations and to find its solution(s).

Sample Question Videos

03:15
02:29

Worksheet • 25 Questions • 2 Videos

Q1:

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.

  • A 8 cm, 16 cm
  • B 4 cm, 8 cm
  • C 3 cm, 13 cm
  • D 3 cm, 22 cm

Q2:

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.
  • A 72 and 9
  • B 75 and 6
  • C 70 and 11
  • D 4 and 8
  • E 71 and 10

Q3:

Four times the weight of Michael is 150 pounds more than the weight of Victoria. Four times the weight of Victoria is 660 pounds less than seventeen times the weight of Michael. Four times the weight of Michael plus the weight of Benjamin equals 290 pounds. Liam would balance all three of the others. Find the weights of the four people.

  • AMichael’s weight = 60 lb, Victoria’s weight = 90 lb, Liam’s weight = 200 lb, Benjamin’s weight = 50 lb
  • BMichael’s weight = 50 lb, Victoria’s weight = 60 lb, Liam’s weight = 90 lb, Benjamin’s weight = 200 lb
  • CMichael’s weight = 90 lb, Victoria’s weight = 60 lb, Liam’s weight = 200 lb, Benjamin’s weight = 50 lb
  • DMichael’s weight = 90 lb, Victoria’s weight = 60 lb, Liam’s weight = 50 lb, Benjamin’s weight = 200 lb
  • EMichael’s weight = 60 lb, Victoria’s weight = 90 lb, Liam’s weight = 50 lb, Benjamin’s weight = 200 lb
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