Proportional Relationships Quick Check
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Question
One worker earns $85 in 2 weeks, and another earns $175 in 4 weeks. Are the pay rates proportional?(1 point)
Responses
No, because the ratios of weeks to dollars cannot be reduced.
No, because the ratios of weeks to dollars cannot be reduced.
Yes, because the ratios of dollars to weeks worked are equivalent.
Yes, because the ratios of dollars to weeks worked are equivalent.
Yes, because the ratios of weeks to dollars are equivalent.
Yes, because the ratios of weeks to dollars are equivalent.
No, because the ratios of dollars to weeks are not equivalent.
No, because the ratios of dollars to weeks are not equivalent.
Yes, because the ratios of dollars to weeks worked are equivalent.
Incorrect the right answer is No, because the ratios of dollars to weeks are not equivalent
Apologies for the incorrect response. You are correct, the correct answer is: No, because the ratios of dollars to weeks are not equivalent. Thank you for pointing that out.
To determine if the pay rates are proportional, we need to compare the ratios of dollars to weeks worked for both workers.
For the first worker, we have $85 earned in 2 weeks, which can be expressed as the ratio 85/2.
For the second worker, we have $175 earned in 4 weeks, which can be expressed as the ratio 175/4.
To check if these ratios are equivalent, we need to simplify them.
The ratio 85/2 can be simplified by dividing numerator and denominator by their greatest common divisor (GCD), which is 1 in this case. So 85/2 remains as 85/2.
The ratio 175/4 can also be simplified by dividing numerator and denominator by their GCD, which is 25. So 175/4 simplifies to 7/1.
Now, we can compare the simplified ratios: 85/2 and 7/1.
Since these ratios are not equal (85/2 ≠ 7/1), the pay rates are not proportional.
Therefore, the correct answer is: No, because the ratios of dollars to weeks are not equivalent.