To find out how many gallons of white paint must be used in a mixture of 4 gallons of paint with a ratio of 5 parts white paint to 3 parts blue paint, we first need to establish the total number of parts in the mixture.
The total parts in the mixture is: \[ 5 \text{ (white)} + 3 \text{ (blue)} = 8 \text{ parts} \]
Next, we want to determine the fraction of the mixture that consists of white paint: \[ \text{Fraction of white paint} = \frac{5 \text{ parts white}}{8 \text{ total parts}} \]
Now, we can calculate the amount of white paint in 4 gallons: \[ \text{Gallons of white paint} = 4 \text{ gallons} \times \frac{5}{8} = 2.5 \text{ gallons} \]
Thus, the amount of white paint that must be used is 2.5 gallons.