David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. How many nachos and sodas did he sell?

35 nachos sold and 52 sodas sold

Step-by-step explanation:

let x represents number of Nachos sold

let y represents number of Sodas sold

We are given two equations, so we can combine them to solve for one variable at a time.

Equation 1: x + y = 87 (because total of both sold was 87 items)

Equatiom 2: 1.50 x + 0.50 y = 78.50 (1.5 times number of nachos, plus 0.50 times number of sodas equals 78.50)

So, y = 87 - x (transpose the n from the first equation)

Take (87 - x) for y in the equation 2

1.50 x + 0.50 (87 - x) = 78.50

1.50 x + 43.50 - 0.50 x = 78.50

1.50 x - 0.50 x + 43.50 = 78.50

x + 43.50 = 78.50

x = 78.50 - 43.50

x = 35

To get the y

y = 87 - 35

y = 52