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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 50 of the programs, and made a profit of $65. How many programs were printed? Letting p represent the number of programs printed, set up an equation that describes this situation. Then solve your equation for p.

User Torv
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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.

User SaphuA
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