You are the captain of the volleyball team and are in charge of ordering t shirts and sweatshirts. T shirts cost $8 and sweatshirts cost $22. If the total cost of the 60 shirts is $872, how many of each did you purchase?

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You are the captain of the volleyball team and are in charge of ordering t shirts and sweatshirts. T shirts cost $8 and sweatshirts cost $22. If the total cost of the 60 shirts is $872, how many of each did you purchase?

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Answer 1 · 2016-10-29T10:17:38

Good communication (explaining what you are doing) is quite important. It could get you extra marks

$There are 28 sweatshirts and 32 T-shirts$ $color(green)("There are 28 sweatshirts and 32 T-shirts")$

Explanation:

2 unknowns means you need 2 equations.

Let the count of sweatshirts be $s$ $s$
Let the count of T Shirts be $t$ $t$

Then we have

$t + s = 60 \leftarrow count$ $t+s=60 larr" count"$ .............Equation(1)

$8 t + 22 s = 872 \leftarrow cost$ $8t+22s=872 larr" cost"$ .......Equation(2)
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The trick is use these so that you only have 1 unknown in 1 equation.

Using Equation(1) $\to t = 60 - s$ $->t=60-s$

Substitute for $t$ $t$ in Equation(2) giving:

$8 (60 - s) + 22 s = 872 \leftarrow Only 1 unknown value, which is s$ $8(60-s)+22s=872 larr" Only 1 unknown value, which is "s$

Multiply out the brackets

$480 - 8 s + 22 s = 872$ $480-8s+22s=872$

$480 + 14 s = 872$ $480+14s=872$

Subtract 480 from both sides

$14 s = 392$ $14s=392$

Divide both sides by 14

$s = 28$ $color(red)(s=28)$

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Substitute for $s$ $s$ in Equation(1) giving

$t + s = 60 \to t + 28 = 60$ $t+s=60" "->" "t color(red)(+28)=60$

Subtract 28 from both sides

$t = 32$ $color(green)(t=32)$

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You are the captain of the volleyball team and are in charge of ordering t shirts and sweatshirts. T shirts cost $8 and sweatshirts cost $22. If the total cost of the 60 shirts is $872, how many of each did you purchase?

1 Answer

Explanation:

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