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?

1 Answer
smendyka
Jun 23, 2018

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

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