Cass decided to sell game programs for the Exeter-Andover field hockey game. The printing cost was 20 cents per program, with a selling price of 59 cents each. Cass sold all but…

Question

asked May 2, 2024 190k views

1 Answer

SaphuA · Answer 1 · 2024-05-08T22:07:11+0000

Answer: 243 game programs

Explanation:

Let's set up an equation to represent the situation:

Cass printed $ p $ game programs.

The printing cost per program is 20 cents, so the total printing cost is $ 0.20p $ dollars.

The selling price per program is 59 cents, or $ 0.59 $ dollars. Cass sold all but 50 programs, so she sold $ p - 50 $ programs.

The profit is the total revenue from sales minus the total printing cost:

Profit = Total Revenue - Total Printing Cost

We're given that Cass made a profit of $65:

$ 65 = (0.59)(p - 50) - 0.20p $

Now, let's solve for $ p $:

First, distribute the 0.59 on the left side:

$ 65 = 0.59p - 29.5 - 0.20p $

Combine like terms:

$ 65 = 0.39p - 29.5 $

Now, add 29.5 to both sides:

$ 65 + 29.5 = 0.39p $

$ 94.5 = 0.39p $

To isolate $ p $, divide both sides by 0.39:

$ \frac{94.5}{0.39} = p $

Now, calculate $ p $:

$ p \approx 242.31 $

Since the number of programs must be a whole number, round up to the nearest whole number:

$ p = 243 $

So, Cass printed 243 game programs.