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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 :

sebasacevedop

Answer:

Marie bought 15 large sweatshirts

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.

[tex]x+y=37 (1)\\289=9x+7y (2)[/tex]

Rewriting equation 1 for x:

[tex]x=37-y[/tex]

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

equation 2:

[tex]289=9(37-y)+7y[/tex]

Simplify and solve the equation for y:

[tex]289 = 333-9y + 7y\\9y-7y = 333-289\\2y = 44\\y = 44/2 = 22[/tex]

Substituting y=22 into

equation 1:

[tex]x + 22 = 37[/tex]

Simplify and solve the equation for x:

[tex]x = 37-22 = 15[/tex]

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

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