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
Oct 29, 2016

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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