The formula for the mark up of an item s:
#p = c + (c * m)#
Where:
#p# is the price of the item after the mark up: $472 for this problem.
#c# is the original cost of the item: what we are solving for in this problem.
#m# is the mark up percent: 18% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 18% can be written as #18/100#.
Substituting and solving for #c# gives:
#$472 = c + (c * 18/100)#
#$472 = (100/100 * c) + 18/100c#
#$472 = 100/100c + 18/100c#
#$472 = (100/100 + 18/100)c#
#$472 = (100 + 18)/100c#
#$472 = 118/100c#
#color(red)(100)/color(blue)(118) xx $472 = color(red)(100)/color(blue)(118) xx 118/100c#
#($47200)/color(blue)(118) = cancel(color(red)(100))/cancel(color(blue)(118)) xx color(blue)(cancel(color(black)(118)))/color(red)(cancel(color(black)(100)))c#
#$400 = c#
The original cost of the set was $400
