Question

Proportionality stands for the y value. Apply your understanding of the constant of proportionality to the questions below:

While training for a marathon, Keith's watch reported how many calories he burned at each mile marker. The data is shown below:

MILES | CALORIES BURNED

2 | 117
1 | 234
3 | 351
4 | 468
5 | 585

Is the number of calories proportional to the number of miles? Explain your thinking.
a) Yes, because every mile is multiplied by 117.
b) No, there is no clear proportionality.
c) Yes, because 117 is subtracted from every mile.
d) The question is not clear.

The next day Keith ran 7.5 miles. How many calories did he burn?
a) He burned 117 calories.
b) He burned 234 calories.
c) He burned 351 calories.
d) He burned 877.5 calories, and I got my answer by multiplying 117 by 7.5.

What is the constant of proportionality?
a) 117
b) 234
c) 351
d) The constant is not provided in the data.

Answer 1

The number of calories burned is proportional to the number of miles run, as each mile corresponds to 117 calories burned. Keith would have burned 877.5 calories running 7.5 miles. The constant of proportionality is 117.

Step-by-step explanation:

The question involves determining the proportionality of calories burned to the number of miles run. To find this, we check if the calories burned per mile are consistent. We find the ratio of calories burned to miles run for each data point:

• For 2 miles, 117 calories per mile (234/2)
• For 1 mile, 234 calories per mile (234/1)
• For 3 miles, 117 calories per mile (351/3)
• For 4 miles, 117 calories per mile (468/4)
• For 5 miles, 117 calories per mile (585/5)

Each mile is consistently associated with 117 calories burned, confirming the proportionality. Therefore, the answer to the first question is:

a) Yes, because every mile is multiplied by 117.

To find the calories burned for 7.5 miles, we multiply the miles by the constant of proportionality:

7.5 miles * 117 calories/mile = 877.5 calories

So, the answer to the second question is:

d) He burned 877.5 calories, and I got my answer by multiplying 117 by 7.5.

The constant of proportionality is the consistent value that relates the two proportional quantities, which in this case is:

a) 117