Question

To raise additional money for the school, the pep club decided to open the concession stand during the tournament and sell sandwiches and bottled water. Club members sold the water for $2 a bottle and the sandwiches for $4 each. They sold a total of 390 items. If they raised $1260 from the concession stand, how many sandwiches did they sell?

They sold
sandwiches.

Answer 1

Let \( x \) be the number of sandwiches sold and \( y \) be the number of bottles of water sold. We can set up the following system of equations based on the information provided:

1. The total number of items sold:
\[
x + y = 390
\]

2. The total amount of money raised:
\[
4x + 2y = 1260
\]

Now we can solve this system of equations.

From the first equation, solve for \( y \):
\[
y = 390 - x
\]

Next, substitute this expression for \( y \) into the second equation:
\[
4x + 2(390 - x) = 1260
\]
Distributing \( 2 \) gives:
\[
4x + 780 - 2x = 1260
\]
Combine like terms:
\[
2x + 780 = 1260
\]
Now, subtract \( 780 \) from both sides:
\[
2x = 1260 - 780
\]
\[
2x = 480
\]
Now, divide both sides by \( 2 \):
\[
x = 240
\]

So, the number of sandwiches sold is \( \boxed{240} \).

To verify, we can find \( y \):
\[
y = 390 - 240 = 150
\]

Now, check the money raised:
\[
4(240) + 2(150) = 960 + 300 = 1260
\]

Both equations are satisfied, confirming that the number of sandwiches sold is indeed \( \boxed{240} \).