Question

you are the senior class president and are selling items for a school fundraiser. you have cell phone cases and t - shirts that have the school logo on them for sale. each case costs $12, and each t - shirt costs $7. after selling a total of 60 items, you have made a total of $450. how many cases and t - shirts were sold? 5 cases, 55 t - shirts 6 cases, 54 t - shirts 54 cases, 6 t - shirts 55 cases, 5 t - shirts

Explanation:

Step1: Set up equations

Let \(x\) be the number of cases and \(y\) be the number of t - shirts.
We have the system of equations:
\(

$$\begin{cases}x + y=60\\12x + 7y=450\end{cases}$$

\)
From the first equation \(y = 60 - x\).

Step2: Substitute and solve

Substitute \(y = 60 - x\) into the second equation:
\(12x+7(60 - x)=450\)
\(12x + 420-7x=450\)
\(5x=450 - 420\)
\(5x = 30\)
\(x = 6\)

Step3: Find \(y\)

Substitute \(x = 6\) into \(y=60 - x\), we get \(y = 60-6=54\)

Answer:

B. 6 cases, 54 t - shirts