Question

HELP ME ASAP! Three students are participating in a walkathon. The data for each student is shown.

Student A: The equation y = 13x represents the amount of money raised (y) for walking (x) miles.

Student B: $36 is raised after walking 3 miles.

Student C:

Miles Walked 4 5
Money Raised $52 $65


Determine which student raised the least amount of money after walking 7 miles.

Answer 1

Student B made the least with $12 with every mile

Explanation:

Student A:

y=13x

y=13(7)

y=91

Student B:

36=3(x)

z=rate

z=12

y=12(x)

y=12(7)

y= 84

Student C:

52=z(4)

z=13

check

65=z(65)

z=13

y=13(x)

y=13(7)

y=91

Answer 2

Student B

Explanation:

You want to know the student who raised the least amount of money walking 7 miles if the money raised by each student is ...

• A: y = 13x; y dollars for x miles
• B: $36 for 3 miles
• C: $52 for 4 miles, $65 for 5 miles

Dollars per mile

The amounts raised for 7 miles can be found either by computing the actual amount for 7 miles, or by comparing the rate in terms of dollars per mile.

A

The equation y = 13x tells you the amount raised increases by $13 for each increase in distance of 1 mile. Student A raises $13 per mile. For 7 miles, they will raise $13·7 = $91.

B

The rate at which student B is raising money is found by dividing dollars by miles:

$36/(3 miles) = $12/mile

Student B raises $12 per mile. For 7 miles, they will raise $12·7 = $84.

C

Student C raises $52/(4 miles) = $13/mile. They will raise the same amount of money for 7 miles that student A does: $91 for 7 miles.

The student raising the least amount of money after walking 7 miles is Student B.

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Additional comment

We note that Student C's rate of $65 for 5 miles is still $65/(5 mi) = $13/mi, the same rate as for 4 miles.

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