Question

Kylie plans to repaint some classroom bookcases. She has 2\frac{3}{4}

4
3
​
gallons of paint. All of the bookcases are the same size and each requires \frac{2}{3}
3
2
​
gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?

Answer 1

4

Explanation:

If n is the number of bookcases to be painted, the number of gallons of paint required is ...

(2/3)n

We want that value not to exceed 2 3/4 gallons, so we have ...

(2/3)n ≤ 2 3/4

n ≤ (3/2)(2 3/4) = (3/2)(2) +(3/2)(3/4)

n ≤ 3 + 9/8 = 4 1/8

The largest integer less than 4 1/8 is 4. Kylie can paint 4 bookcases with the available paint.