Frances left a 21​% tip on a meal. Including the​ tip, its cost was​ 42.35. What was the cost of the meal before the​ tip?

1 Answer
Feb 11, 2018

See a solution process below:

Explanation:

The formula for finding the total cost of an item including tip is:

#t = p + (p * r)#

Where:

#t# is the total price of the item: 42.35 for this problem.

#p# is the original price of the item: what we are solving for in this problem.

#r# is the rate of the tip: 21% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 21% can be written as #21/100#.

Substituting and solving for #p# gives:

#42.35 = p + (p xx 21/100)#

#42.35 = 1p + 21/100p#

#42.35 = 100/100p + 21/100p#

#42.35 = (100/100 + 21/100)p#

#42.35 = 121/100p#

#color(red)(100)/color(blue)(121) xx 42.35 = color(red)(100)/color(blue)(121) xx 121/100p#

#4235/color(blue)(121) = cancel(color(red)(100))/cancel(color(blue)(121)) xx color(blue)(cancel(color(black)(121)))/color(red)(cancel(color(black)(100)))p#

#35 = p#

The cost of the meal before the tip was 35.00