Question

$30 was saved after 3 weeks, and $50 was saved after 10 weeks. Are these rates or ratios equivalent? Explain your answer.

A) Yes, they are equivalent rates.
B) No, they are not equivalent rates.
C) Yes, they are equivalent ratios.
D) No, they are not equivalent ratios.

Answer 1

The rates are $10 per week for the first scenario and $5 per week for the second scenario. Since these rates are not equal, they are not equivalent rates, nor equivalent ratios. The correct answer is D) No, they are not equivalent ratios.

Step-by-step explanation:

To determine if the rates or ratios are equivalent, we calculate the savings per week in both scenarios and compare them. For the first scenario, $30 was saved over 3 weeks, which gives us a rate of $10 per week (30/3). In the second scenario, $50 was saved over 10 weeks, which gives us a rate of $5 per week (50/10).

Since $10 per week is not equal to $5 per week, it is clear that these are not equivalent rates. Nor are they equivalent ratios, as the proportion of dollars saved per week is different in each case (10:3 is not equivalent to 5:10).

Therefore, the correct answer is D) No, they are not equivalent ratios.