Adam plans to repaint some classroom bookcases. He has 3, one half3

2
1

gallons of paint. All of the bookcases are the same size and each requires one fifth
5
1

gallon of paint. What is the maximum number of complete bookcases he can paint?

1 answer

To determine how many complete bookcases Adam can paint, we first need to convert the amount of paint he has into a single unit. Adam has 3.5 gallons of paint (which can also be expressed as \( \frac{7}{2} \) gallons).

Next, we know that each bookcase requires \( \frac{1}{5} \) gallon of paint.

To find the maximum number of bookcases Adam can paint, we can divide the total amount of paint by the amount of paint needed for each bookcase:

\[ \text{Number of bookcases} = \frac{\text{Total paint}}{\text{Paint per bookcase}} = \frac{3.5}{\frac{1}{5}} \]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \text{Number of bookcases} = 3.5 \times 5 = 17.5 \]

Since Adam cannot paint half of a bookcase, we take the maximum whole number, which is 17.

Therefore, the maximum number of complete bookcases Adam can paint is \( \boxed{17} \).