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Determine if each pair of ratios is equivalent. Explain your reasoning.

a. 15 minutes to read 9 pages; 50 minutes to read 30 pages
b. Lusita earned $85 for 8 hours of babysitting. Avery earned $125 for 11 hours of babysitting. Are the rates equivalent? Explain.
c. Miss Ferguson recorded 17 absences in her class during the first 30 days of school. During the last 60 days of school, she recorded 42 absences. Are the rates equivalent? Explain.

User Atasha
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1 Answer

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Final answer:

To determine if the ratios are equivalent, we calculate the unit rates for each scenario. In case a, the unit rates for reading pages per minute are equivalent; in case b, the babysitting rates per hour are not equivalent; and in case c, the rates of absences per day are not equivalent.

Step-by-step explanation:

To determine if each pair of ratios is equivalent, we compare the ratios after converting them to simpler forms or unit rates.

a. 15 minutes to read 9 pages; 50 minutes to read 30 pages

First, calculate the unit rate for each ratio by dividing the number of pages by the number of minutes:

For the first ratio: 9 pages / 15 minutes = 0.6 pages per minute

For the second ratio: 30 pages / 50 minutes = 0.6 pages per minute

Since both unit rates are the same, we can conclude that these two ratios are equivalent.

b. Lusita earned $85 for 8 hours of babysitting. Avery earned $125 for 11 hours of babysitting.

Again, calculate the unit rate for each situation:

For Lusita: $85 / 8 hours = $10.625 per hour

For Avery: $125 / 11 hours = $11.36 per hour

The unit rates differ, indicating that the rates are not equivalent.

c. Miss Ferguson recorded 17 absences in her class during the first 30 days of school. During the last 60 days of school, she recorded 42 absences.

Calculate the rate of absences per day:

For the first period: 17 absences / 30 days = 0.567 absences per day

For the second period: 42 absences / 60 days = 0.7 absences per day

These rates are different; thus, the rates of absences are not equivalent.

User Shidhin Cr
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