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Last week, Keegan bought 4 shirts and 9
hats for a total of $108.
Today, Keegan bought 17 shirts and 21 hats
for a total of $321.
Assuming neither item has changed in price,
what is the cost of a shirt in dollars?
to write down notes or work through problems

Respuesta :

rspill6

Answer:  Shirts are $9 each and hats are $8 each

Step-by-step explanation:

Let S be the price of a Shirt, and H the price of a Hat.

First Week:  4S + 9H = $108

Today:         17S + 21H = $321

We have 2 equations and 2 unknowns (S and H).  Rearrange one of the equations to isolate one of the unknowns.  I'll rearrange the first for S:

4S + 9H = $108

4S  = $108 - 9H

S =  ($108 - 9H)/4

S = 27 - 2.25H

Now use this value of S in the second equation:

17S + 21H = $321

17(($27 - 2.25H) + 21H = $321

Solve for H:

459 -38.25H + 21H = $321

-17.25H = - 138

H = $8

Each hat was $8.

Use this value in the first equation to find S:

4S + 9H = $108

4S + 9*($8) = $108

4S + $72 = $108

S = $9

Each shirt was $9.

==

Check to see if the numbers give the correct results:

4*($9) + 9*($8) = $108

17*($9) + 21*($8) = $321

Both yield the correct amounts. Shirts are $9 each and hats are $8 each.

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