Question

A certain mixed paint only calls for 33 gallons of red paint and 88 gallons of black paint. Write a part-to-part ratio of red paint to black paint. Then write a part-to-whole ratio of red paint to the total gallons of mixed paint. Finally, write a fraction in simplest terms to express the proportion of red paint to the whole.

Answer 1

To find the part-to-part ratio of red paint to black paint, we take the amount of red paint and the amount of black paint.

1. **Part-to-part ratio of red paint to black paint**:
- Red Paint: 33 gallons
- Black Paint: 88 gallons
- Part-to-part ratio: \( 33 : 88 \)

To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which is 11:

\[
33 \div 11 = 3 \quad \text{and} \quad 88 \div 11 = 8
\]

So, the simplified part-to-part ratio of red paint to black paint is:

\[
3 : 8
\]

2. **Part-to-whole ratio of red paint to total gallons of mixed paint**:
- Total paint = Red paint + Black paint = \( 33 + 88 = 121 \) gallons
- The part-to-whole ratio of red paint to total gallons is:

\[
33 : 121
\]

3. **Fraction in simplest terms to express the proportion of red paint to the whole**:
- The fraction representing the proportion of red paint to the total mixed paint is:

\[
\frac{33}{121}
\]

Since 33 and 121 have no common factors (other than 1), this fraction is already in simplest form.

Thus, the answers are:
- Part-to-part ratio: \( 3 : 8 \)
- Part-to-whole ratio: \( 33 : 121 \)
- Fraction: \( \frac{33}{121} \)