Q42. - Algebra 1

Question

PAINT Joel used a half-gallon of paint to cover 84 square feet of wall. He has 932 square feet of wall to paint. How many gallons of paint should he purchase?

Step-by-Step Solution

Answer

The number of gallons of paint needed are .

Step 1. Write down the given statement.

It is given that half-gallon covers 84 square feet.

Therefore 1 complete gallon will cover:

 $$\begin{gathered} =84\left(2\right) \\ =168\text{ sq. feet} \end{gathered}$$

Step 2. By method of proportion.

Let the total number of gallons of paint be x. Therefore the proportion can be written as:

 $$\begin{gathered} \frac{1}{168}=\frac{x}{932} \\ 168\left(x\right)=1\left(932\right) \\ 168x=932 \\ \frac{168x}{168}=\frac{932}{168} \\ x=5.55\text{\hspace{0.17em}gallons} \end{gathered}$$

Step 3. Conclusion for the number of gallons needed.

The number of gallons of paint needed are $x=5.55\text{\hspace{0.17em}gallons}$.