Question

One group of students has 15 blue pencils and 45 red pencils. Another group of students has 30 blue pencils and 90 red pencils. What proportion describes the relative amount of each color of pencils in each group?

Answer 1

To determine the proportions of each color of pencils in each group, we need to calculate the total number of pencils in each group first and then find the proportions for blue and red pencils.

**Group 1:**
- Blue pencils: 15
- Red pencils: 45

Total pencils in Group 1:
\[
15 + 45 = 60
\]

Proportion of blue pencils in Group 1:
\[
\text{Proportion of blue} = \frac{\text{Number of blue pencils}}{\text{Total pencils}} = \frac{15}{60} = \frac{1}{4}
\]

Proportion of red pencils in Group 1:
\[
\text{Proportion of red} = \frac{\text{Number of red pencils}}{\text{Total pencils}} = \frac{45}{60} = \frac{3}{4}
\]

**Group 2:**
- Blue pencils: 30
- Red pencils: 90

Total pencils in Group 2:
\[
30 + 90 = 120
\]

Proportion of blue pencils in Group 2:
\[
\text{Proportion of blue} = \frac{30}{120} = \frac{1}{4}
\]

Proportion of red pencils in Group 2:
\[
\text{Proportion of red} = \frac{90}{120} = \frac{3}{4}
\]

**Summary of Proportions:**

- Group 1: Blue = \( \frac{1}{4} \), Red = \( \frac{3}{4} \)
- Group 2: Blue = \( \frac{1}{4} \), Red = \( \frac{3}{4} \)

Both groups have the same proportions of blue and red pencils:
- Blue pencils: \( \frac{1}{4} \)
- Red pencils: \( \frac{3}{4} \)