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.
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.
Answers
GPT-4o mini
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.
### 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.