Question

Thomas has some leftover paint that he would like to sell He mixes three over a gallon of blue paint with six five over a gallons of white paint then he pours this light blue mixture into one over 4 gallons containers to find out how many of these 1/4 gallons containers he can fill which two equations would you need A 4 3/8 + 6 5/8 = 11 B 1/4 * 11 = 2 3/4 C 11 / 1/4 equal 44 D4 3/8 + 6 5/8 + 2/8 = 11 1/4

Answer 1

To solve the problem, let's first determine the total amount of paint Thomas has after combining the blue and white paint.

Thomas mixes:
- \(3 \frac{1}{8}\) gallons of blue paint
- \(6 \frac{5}{8}\) gallons of white paint

First, we need to convert these mixed fractions to improper fractions or decimals for easier addition.

1. **Convert mixed numbers to improper fractions:**
- \(3 \frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8}\)
- \(6 \frac{5}{8} = \frac{6 \times 8 + 5}{8} = \frac{48 + 5}{8} = \frac{53}{8}\)

2. **Add the two fractions:**
\[
\frac{25}{8} + \frac{53}{8} = \frac{25 + 53}{8} = \frac{78}{8} = \frac{39}{4} = 9 \frac{3}{4} \text{ gallons}
\]

Now we have \(9 \frac{3}{4}\) gallons of paint, which is equivalent to \(9.75\) gallons if we convert it to decimal.

3. **Find out how many \( \frac{1}{4}\) gallon containers can be filled:**
To do this, we divide the total gallons by the size of each container:
\[
9.75 \div \frac{1}{4} = 9.75 \times 4 = 39
\]

Thus, Thomas can fill 39 containers of \( \frac{1}{4} \) gallon each.

Now, let's evaluate the provided equations to see which two relate to our findings:

- **A**: \(4 \frac{3}{8} + 6 \frac{5}{8} = 11\) ➔ This is incorrect since it does not represent the total paint.
- **B**: \(1/4 \times 11 = 2 \frac{3}{4}\) ➔ This is incorrect; it doesn’t relate to the total gallons of paint.
- **C**: \(11 \div \frac{1}{4} = 44\) ➔ This seems incorrect since our total was actually \(9 \frac{3}{4}\), not \(11\).
- **D**: \(4 \frac{3}{8} + 6 \frac{5}{8} + \frac{2}{8} = 11 \frac{1}{4}\) ➔ This is also incorrect because the calculations yield the total that we computed, however, its representation does not directly equal the total gallons we calculated.

Based on the calculations, you didn't present correct equations that represent the results obtained. However, the correct approach consists of summing the paints, converting mixed numbers, and then calculating how many \( \frac{1}{4} \) gallon containers can be filled from the total.

The relevant equation for identifying the total gallons from the mixture would have ideally been shown, therefore none of the provided equations accurately represent the situation described based on your question.