Question

Matthew is training to participate in a half marathon. Each week, Matthew increases the number of miles he runs in the previous week by the same percent. The table below shows the number of miles he runs in weeks 1 and 2.

Week Number of Miles Run
1 12.5
2 15.5

Complete the sentence. Do not round your answer.
Matthew runs ____ miles in week 3.

Answer 1

Answer:14.58 miles.

Step-by-step explanation:

Matthew is training to participate in a half marathon.

The distance covered by Matthew on the first day is 12.5 miles.

The distance covered by Matthew on the second day is 13.5 miles.

The distance increased on the second day is, 13.5-12.5=1 mile.

The percentage will be,

=\dfrac{1}{12.5}\times 100\%

=0.08\times 100\%

=8\%

Hence, each day he runs 8% more. So the distance covered by him on day 3 will be,

=13.5+\left(13.5\times \dfrac{8}{100}\right)

=13.5+1.08

=14.58 miles

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Step-by-step explanation:

Answer 2

Answer:

Basic consensus is that that other answer is wrong. The actual answer is 19.22

Step-by-step explanation:

To find the common ratio you just do this, last number = 15.5, and first number = 12.5.

15.5/12.5 equals 1.24.

^That's the common ratio.^

using A(n) = a * r ^ n - 1,

you get 12.5 * 1.24 ^ 3 - 1, or just 12.5 * 1.24 ^ 2

and solving that problem, you get 19.22.

Confirm this by doing the same thing earlier, 19.22/15.5 is 1.24. Which is the ratio found earlier. So it checks out.