Question

Are these ratios equivalent?

33 packages : 41 hours

46 packages : 53 hours

Answer 1

To determine if the ratios \( 33 \text{ packages} : 41 \text{ hours} \) and \( 46 \text{ packages} : 53 \text{ hours} \) are equivalent, we can express each ratio as a fraction and compare them:

1. For the first ratio:
\[
\text{Ratio 1} = \frac{33 \text{ packages}}{41 \text{ hours}} \approx 0.8049
\]

2. For the second ratio:
\[
\text{Ratio 2} = \frac{46 \text{ packages}}{53 \text{ hours}} \approx 0.8679
\]

Now, let's check if the two ratios are equal by cross-multiplying:

\[
33 \times 53 \quad \text{and} \quad 41 \times 46
\]

Calculating each:

- \( 33 \times 53 = 1749 \)
- \( 41 \times 46 = 1886 \)

Since \( 1749 \neq 1886 \), the two ratios \( 33 : 41 \) and \( 46 : 53 \) are not equivalent.