To find out how many 1/4 gallon containers Thomas can fill with his paint mixture, we first need to calculate the total amount of paint he has by adding the quantities of blue and white paint together.
- Add the blue paint and the white paint:
- Blue paint: \(4 \frac{3}{8} \text{ gallons}\)
- White paint: \(6 \frac{1}{8} \text{ gallons}\)
We need to convert these mixed numbers into improper fractions to add them easily.
-
Blue paint: \[ 4 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8} \]
-
White paint: \[ 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} \]
Now, we add the two fractions: \[ \frac{35}{8} + \frac{49}{8} = \frac{35 + 49}{8} = \frac{84}{8} \]
We can simplify \( \frac{84}{8} \): \[ \frac{84 \div 4}{8 \div 4} = \frac{21}{2} = 10 \frac{1}{2} \text{ gallons} \]
- Now, we need to find out how many 1/4 gallon containers can be filled with \( 10 \frac{1}{2} \) gallons of paint. First, we convert \( 10 \frac{1}{2} \) into an improper fraction: \[ 10 \frac{1}{2} = \frac{10 \times 2 + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2} \]
The number of 1/4 gallon containers that can be filled is given by dividing the total gallons by \( \frac{1}{4} \): \[ \frac{21/2}{1/4} = \frac{21}{2} \times 4 = \frac{21 \times 4}{2} = \frac{84}{2} = 42 \]
Therefore, Thomas can fill 42 containers of 1/4 gallon completely with his paint mixture.
The answer is 42.