Question

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?

Answer 1

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

`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`
Let the count of T Shirts be `t`

Then we have

`t+s=60 larr" count"`.............Equation(1)

`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) `->t=60-s`

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

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

Multiply out the brackets

`480-8s+22s=872`

`480+14s=872`

Subtract 480 from both sides

`14s=392`

Divide both sides by 14

`color(red)(s=28)`

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Substitute for `s` in Equation(1) giving

`t+s=60" "->" "t color(red)(+28)=60`

Subtract 28 from both sides

`color(green)(t=32)`

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