Answer: Each shirt is $29 while each sweater is $53.
Step-by-step explanation: The first step is to identify the clues in the question. Let each shirt be represented by letter ‘h’ and each sweater be represented by letter ‘w.’
If the cost of a sweater is 5 less than twice the price of a shirt, then the price of a sweater can be expressed as,
2h -5.
So we have
w = 2h - 5 ———(1)
If four shirts and three sweaters cost $275, we then have the expression,
4h + 3w = 275 ———(2)
Substitute for the value of w into equation (2)
4h + 3(2h - 5) = 275
4h + 6h - 15 = 275
10h - 15 = 275
Add 15 to both sides of the equation
10h = 290
Divide both sides of the equation by 10
h = 29.
Having calculated the value of h, we now substitute for the value of h into equation (1)
w = 2h - 5
w = 2(29) - 5
w = 58 - 5
w = 53
Therefore each shirt costs $29 while each sweater costs $53.
