Question

For a school fundraiser, Tory sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50.Write a system of equations which represents this situation.A. 28p + 17p and 40c + 20c = 160.50Can you show me how to solve this? break it down please?

Answer 1

The first thing we have to do is identify what our variables are

$\begin{gathered} P\to\text{Popcorn} \\ C\to\text{Candy} \end{gathered}$

Now we want to know how much a bag of Popcorn is worth and how much a candy bar is worth.

For this we have 2 equations one for what Tory sold and another for what Jake sold

$\begin{gathered} 28P+40C=282\to\text{Tory} \\ 28P=282-40C \\ P=\frac{282-40C}{28} \end{gathered}$$\begin{gathered} 17P+20C=160.50\to\text{Jake} \\ 17P=160.50-20C \\ P=\frac{160.50-20C}{17} \end{gathered}$

From the 2 equations we solve for P, then we equalize them to be able to find the value of C

$\begin{gathered} \frac{282-40C}{28}=\frac{160.50-20C}{17} \\ 17(282-40C)=28(160.50-20C) \\ 4794-680C=4494-560C \\ 680C-560C=4794-4494 \\ 120C=300 \\ C=\frac{300}{120} \\ C=\frac{5}{2} \\ C=2.5 \end{gathered}$

Now we know that a candy bar costs $ 2.5 we use any of the initial equations to find the value of the price of bags of popcorn

$\begin{gathered} P=\frac{282-40(\frac{5}{2})}{28} \\ P=\frac{282-100}{28} \\ P=\frac{182}{28} \\ P=\frac{13}{2} \\ P=6.5 \end{gathered}$

So the answer is: The value of a bag of popcorn is $6.5 and that of a candy bar is $ 2.5