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Math  /  Algebra

QuestionYou buy painting supplies for $12\$ 12, and you charge $3\$ 3 per person to paint faces. How many faces will you need to paint to earn $15\$ 15 in profit? CLEAR CHECK
Write an equation to represent the problem. Let ff represent the number of faces you need to paint. □\square f- □\square
How many faces do you need to paint? You need to paint □\square faces.

Studdy Solution

STEP 1

1. The cost of painting supplies is 12.<br/>2.Youcharge12.<br />2. You charge 3 per person for face painting.
3. You want to earn $15 in profit.
4. We need to find the number of faces to paint to achieve this profit.

STEP 2

1. Define the variables.
2. Write an equation to represent the problem.
3. Solve the equation for the number of faces.

STEP 3

Define the variables.
Let f f represent the number of faces you need to paint.

STEP 4

Write an equation to represent the problem.
The total revenue from painting f f faces is 3f 3f dollars. To earn a profit of 15,therevenuemustexceedthecostofsuppliesby15, the revenue must exceed the cost of supplies by 15.
3f−12=15 3f - 12 = 15

STEP 5

Solve the equation for the number of faces.
Add 12 to both sides of the equation to isolate the term with f f :
3f=15+12 3f = 15 + 12 3f=27 3f = 27
Divide both sides by 3 to solve for f f :
f=273 f = \frac{27}{3} f=9 f = 9
You need to paint 9 \boxed{9} faces.

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