Question

AYSO has 18 8th grade boys’ teams this year, but this is a 28% (rounded to the nearest whole number) decrease from the prior year. How many 8th grade teams were there last year?

Answer 1

See a solution process below:

Explanation:

The formula for calculating the percent change in a value between two points in time is:

`p = (N - O)/O * 100`

Where:

`p` is the percent change - -28% for this problem.

`N` is the New Value - 18 in this problem.

`O` is the Old Value - what we are solving for in this problem.

Substituting and solving for `O` gives:

`-28 = (18 - O)/O * 100`

`-28 = (18/O - O /O) * 100`

`-28 = (18/O - 1) * 100`

`-28 = (18/O * 100) - (1 * 100)`

`-28 = 1800/O - 100`

`-28 + color(red)(100) = 1800/O - 100 + color(red)(100)`

`72 = 1800/O - 0`

`72 = 1800/O`

`color(red)(O)/color(blue)(72) xx 72 = color(red)(O)/color(blue)(72) xx 1800/O`

`color(red)(O)/cancel(color(blue)(72)) xx color(blue)(cancel(color(black)(72))) = cancel(color(red)(O))/color(blue)(72) xx 1800/color(red)(cancel(color(black)(O)))`

`O = 1800/color(blue)(72)`

`O = 25`

Last year there were `color(red)(25)` 8th grade Teams