A clothing store sells t-shirts, t, for $8 a shirt, shorts, s, for $12, and hats, h, for $10 each. The store earned $464 revenue last month. The store sold three times as many T-shirts than hats, and twice as many shorts as hats. Using the substitution method, how many t-shirts, shorts, and hats did the store sell?

Question

Wolf

Mathematics

14 May, 03:47

A clothing store sells t-shirts, t, for $8 a shirt, shorts, s, for $12, and hats, h, for $10 each. The store earned $464 revenue last month. The store sold three times as many T-shirts than hats, and twice as many shorts as hats. Using the substitution method, how many t-shirts, shorts, and hats did the store sell?

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Ethan Rush · Answer 1

Let x be the variable for a t-shirt for $8.

Let y be the variable for shorts for $12.

Let z be the variable for the hats that cost $10 each.

We have the expression 1 below:

$464 = $8x + $12y + $10z

other expressions:

3z = x

2z = y

By substitution we can solve each variable:

464 = 8 (3z) + 12 (2z) + 10z

464 = 24z + 24z + 10z

464 = 58z

z = 8

Solve for x andy:

3z=x

3*8 = 24=x

2z=y

2*8 = 16 = y

The t-shirts are 24 pieces, the shorts are 16 pieces and hats are 8 pieces.