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Sagot :
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
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