Question

Jenna mixed two shades of purple paint. For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint. For Purple Majesty, she used a blue to red paint ratio of 7 to 4. Compare the ratios of red paint to blue paint.

The ratio for Purple People Eater can be expressed in fraction form as
.
The ratio for Purple Majesty can be expressed in fraction form as
.
To compare these fractions, rewrite them with a common denominator of
.
The ratio of red paint to blue paint in Purple People Eater is
the ratio in Purple Majesty.

Answer 1

To analyze the two shades of purple paint used by Jenna, we start by converting their paint ratios into fraction form.

### Purple People Eater
For Purple People Eater, the ratio of red paint to blue paint is given as:
- Red : Blue = 3 : 5

We can express this as a fraction:
\[
\text{Ratio for Purple People Eater} = \frac{3 \text{ (red)}}{5 \text{ (blue)}}
\]

### Purple Majesty
For Purple Majesty, the ratio of blue to red paint is given as:
- Blue : Red = 7 : 4

Since we want the ratio of red to blue, we can express it as:
\[
\text{Ratio for Purple Majesty} = \frac{4 \text{ (red)}}{7 \text{ (blue)}}
\]

### Common Denominator
Now we need to compare these two fractions:
- Purple People Eater: \( \frac{3}{5} \)
- Purple Majesty: \( \frac{4}{7} \)

To compare these fractions, we will find a common denominator. The denominators are 5 and 7. The least common multiple (LCM) of 5 and 7 is 35.

Now, we rewrite both fractions with a common denominator of 35:
1. For Purple People Eater:
\[
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\]

2. For Purple Majesty:
\[
\frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
\]

### Comparing the Ratios
Now we compare:
- Purple People Eater: \( \frac{21}{35} \)
- Purple Majesty: \( \frac{20}{35} \)

Since \( \frac{21}{35} \) is greater than \( \frac{20}{35} \), we conclude that:
The ratio of red paint to blue paint in Purple People Eater is **greater than** the ratio in Purple Majesty.

### Summary
1. The ratio for Purple People Eater can be expressed in fraction form as \( \frac{3}{5} \).
2. The ratio for Purple Majesty can be expressed in fraction form as \( \frac{4}{7} \).
3. The common denominator is \( 35 \).
4. The ratio of red paint to blue paint in Purple People Eater is greater than the ratio in Purple Majesty.