Question

Marie bought a total of 37 sweatshirts for her soccer team spending a total of $289. Some sweatshirts were large, the rest small. If the large sweatshirts cost $9 each and the small sweatshirts cost $7 each, how many large sweatshirts did she buy?

Answer 1

Marie bought 15 large sweatshirts

Step-by-step explanation:

In this case we have 2 equations with two unknowns, x and y, which represent the number of sweatshirts of $ 9 and $ 7 respectively.

`x+y=37 (1)\\289=9x+7y (2)`

Rewriting equation 1 for x:

`x=37-y`

Using the substitution method, substituting x = 37-y into

equation 2:

`289=9(37-y)+7y`

Simplify and solve the equation for y:

`289 = 333-9y + 7y\\9y-7y = 333-289\\2y = 44\\y = 44/2 = 22`

Substituting y=22 into

equation 1:

`x + 22 = 37`

Simplify and solve the equation for x:

`x = 37-22 = 15`

Therefore Marie bought 15 large sweatshirts and 22 small sweatshirts with his $289