Question

There were 25 runners competing in a race. The number of runners who finished ahead of Paula was one-third the number of runners who finished after her. In what place did Paula finish?

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Answer 1

7th Place

Explanation:

Seeing as how the number of runners in front of Paula is
`(1)/(3)` the number of runners behind her,

Assign the number of people behind Paula to a variable:

# of people behind Paula = b, which means

# of people ahead of Paula =
`(1)/(3)` b

Use the variable to make an equation:

b (people behind Paula) +
`(1)/(3)` b (people ahead of Paula) + 1 (Paula) = 25

b +
`(1)/(3)` b + 1 = 25

Solve for b:

b +
`(1)/(3)` b + 1 = 25

b +
`(1)/(3)` b = 24

`(4)/(3)` b = 24

b = 18

If there are 18 people behind Paula, there are
`(1)/(3)` * 18 people in front of her, which is 6; This puts Paula in 7th place.