Question

A tire store sold two types of tires, a sports tire and an all-season tire. The sum of  six times the sports tire and five times the all-season tire is 93, and the difference  between three-quarters of the sports tire and two-thirds of the all-season tires is zero. For the store manager, find the number of each type of tire sold in one day (3  marks).​

Answer 1

9514 1404 393

Answer:

  8 sports tires and 9 all-season tires were sold

Step-by-step explanation:

If we let x and y represent the numbers of sports tires and all-season tires sold, respectively, then the problem statement tells us ...

  6x +5y = 93

  3/4x -2/3y = 0

These equations can be solved by your favorite method to find ...

  x = 8

  y = 9

8 sports and 9 all-season tires were sold.

_____

Additional comment

My favorite method for solving systems of linear equations is a graphing calculator (when solutions are expected to be integers). If you want to do this "by hand", you can multiply the second equation by -8 and add the result to the first equation.

  (6x +5y) -8(3/4x -2/3y) = (93) -8(0)

  31/3y = 93

  y = 9

  3/4x = 6  ⇒  x = 8 . . . . substitute for y in the second equation

  (sports, all-season) = (8, 9)