Question

There were 21 runners competing in a race. The number of runners who finished ahead of Marsha was one-fourth the number of runners who finished after her. In what place did Marsha finish?

Answer 1

Marsha finished in 5th place in the race. This was determined by setting up an equation representing the fact that the number of runners who finished before her was one-fourth of those who finished after her.

Step-by-step explanation:

To find the place Marsha finished in the race, we need to set up a simple algebraic equation based on the information provided:

• The number of runners who finished ahead of Marsha is one-fourth the number of runners who finished after her.

Let's denote the number of runners who finished ahead of Marsha as A, and the number of runners who finished after her as B. Since there were a total of 21 runners, and considering Marsha herself, the relationship can be expressed as follows:

A + B + 1 = 21

It is given that the number of runners ahead of Marsha (A) is one-fourth of the number of runners after her (B), so:

A = B/4

Substituting A in the first equation:

B/4 + B + 1 = 21

Combining like terms and multiplying through by 4 to eliminate fractions:

B + 4B + 4 = 84

5B + 4 = 84

5B = 80

B = 16

Now we know B, we can find A:

A = B/4

A = 16/4

A = 4

Since A is the number of runners ahead of Marsha, she finished in 5th place.