Question

The table shows that the ratio of boys to girls at Midtown Middle School is 3 to 4.

A 2-column table with 4 rows. Column 1 is labeled Boys with entries 3, 12, 15, 75. Column 2 is labeled Girls with entries 4, question mark, question mark, question mark.

Which classes have an equivalent ratio of boys to girls? Check all that apply.

a math class with 12 boys and 16 girls
an English class with 14 boys and 14 girls
a science class with 15 boys and 20 girls
a Spanish class with 20 boys and 15 girls
a band class with 75 boys and 100 girls

Answer 1

To determine which classes have an equivalent ratio of boys to girls of 3 to 4, we can set up the ratio for each class and check if it simplifies to 3/4.

The ratio of boys to girls is expressed as:

\[
\text{Ratio} = \frac{\text{Boys}}{\text{Girls}} = \frac{3}{4}
\]

We can check each class:

1. **Math class with 12 boys and 16 girls:**
\[
\frac{12}{16} = \frac{3}{4} \quad \text{(Equivalent)}
\]

2. **English class with 14 boys and 14 girls:**
\[
\frac{14}{14} = 1 \quad \text{(Not equivalent)}
\]

3. **Science class with 15 boys and 20 girls:**
\[
\frac{15}{20} = \frac{3}{4} \quad \text{(Equivalent)}
\]

4. **Spanish class with 20 boys and 15 girls:**
\[
\frac{20}{15} = \frac{4}{3} \quad \text{(Not equivalent)}
\]

5. **Band class with 75 boys and 100 girls:**
\[
\frac{75}{100} = \frac{3}{4} \quad \text{(Equivalent)}
\]

**Classes with an equivalent ratio of boys to girls (3 to 4):**

- Math class with 12 boys and 16 girls
- Science class with 15 boys and 20 girls
- Band class with 75 boys and 100 girls

So, the correct classes that have an equivalent ratio of boys to girls are the Math class, Science class, and Band class.