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A clothing store sells T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each. The store earned $406 in 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?

Respuesta :

MathPhys

Step-by-step explanation:

From the total revenue, we know that:

8t + 12s + 10h = 406

We're also told:

t = 3h

s = 2h

If we substitute these for t and s:

8 (3h) + 12 (2h) + 10h = 406

24h + 24h + 10h = 406

58h = 406

h = 7

Now we can find t and s:

t = 3h = 21

s = 2h = 14

The store sold 21 T-shirts, 14 shorts, and 7 hats.

The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each and stored earn $406

So,

8t + 12s + 10h = 406

And

the store sold three times as many T-shirts than hats

So,

t = 3h

And

twice as many shorts as hats.

s = 2h

By substituting t and s into the equation first

8(3h) + 12(2h) + 10h = 406

h = 7

Now

t = 21 and s = 14.

Hence, The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.

For more about the equation,

https://brainly.com/question/10413253

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