Question

Are these ratios equivalent?

69 items every 78 seconds

46 items every 97 seconds

Answer 1

To determine if the two ratios are equivalent, we can compare the rates of items per second for each case.

1. **First ratio**: 69 items every 78 seconds
- Rate = \( \frac{69 \text{ items}}{78 \text{ seconds}} \)

2. **Second ratio**: 46 items every 97 seconds
- Rate = \( \frac{46 \text{ items}}{97 \text{ seconds}} \)

Now we can calculate each rate.

**First Ratio:**
\[
\frac{69}{78} \approx 0.8846153846 \text{ items per second}
\]

**Second Ratio:**
\[
\frac{46}{97} \approx 0.4742260062 \text{ items per second}
\]

Since \( 0.8846153846 \) is not equal to \( 0.4742260062 \), the two ratios are not equivalent.

Thus, **the ratios are not equivalent**.