# 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 $\textcolor{g r e e n}{\text{There are 28 sweatshirts and 32 T-shirts}}$#### 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 $t + s = 60 \leftarrow \text{ count}$.............Equation(1) $8 t + 22 s = 872 \leftarrow \text{ cost}$.......Equation(2) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The trick is use these so that you only have 1 unknown in 1 equation. Using Equation(1) $\to t = 60 - s$Substitute for $t$in Equation(2) giving: $8 \left(60 - s\right) + 22 s = 872 \leftarrow \text{ Only 1 unknown value, which is } s$Multiply out the brackets $480 - 8 s + 22 s = 872$$480 + 14 s = 872$Subtract 480 from both sides $14 s = 392$Divide both sides by 14 $\textcolor{red}{s = 28}$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Substitute for $s$in Equation(1) giving $t + s = 60 \text{ "->" } t \textcolor{red}{+ 28} = 60$Subtract 28 from both sides $\textcolor{g r e e n}{t = 32}\$

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