Are these ratios equivalent?

Question

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.