Question

A clothing store sells T-shirts for one price and sweatshirts for a different price. The cost of 5 T- Shirts is the same as the cost of 3 sweatshirts. If he spent a total of $240.00 on the 10 T-shirts and 9 sweatshirts, what was the cost of each sweatshirt?

Answer 1

System of Equations

To solve this problem, let's set the following variables:

x = cost of one T-shirt

y = cost of one sweatshirt

We are given two conditions: The cost of 5 T-shirts is the same as the cost of 3 sweatshirts. Expressing the condition as an equation:

5x = 3y

The other condition is that for 10 T-shirts and 9 sweatshirts, the total cost was $240. Now we write the second equation:

10x + 9y = 240

It's required to find the cost of each sweatshirt (variable y). Let's rearrange the first equation and write down the second equation:

5x - 3y = 0 [1]

10x + 9y = 240 [2]

We'll use the elimination method. Multiplying [1] by -2:

-10x + 6y = 0

Adding this new equation with [2], the variable x cancels out:

15y = 240

Dividing by 15:

y = 240/15 = 16

The cost of each sweatshirt is $16