SOLUTION: The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the m

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Question 1204027: The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the mother, respectively?
Answer by greenestamps(13200) About Me  (Show Source):
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Let's look at two different ways to set the problem up using a single variable. We could use two variables; but the work required to reach the answer is usually easier if we use a single variable.

Probably the standard approach...

let x = daughter's age
then 56-x = mother's age (the sum of their ages is 56)

x+4 = daughter's age in 4 years
(56-x)+4 = 60-x = mother's age in 4 years

In 4 years, the mother's age will be 3 times the daughter's age:

60-x = 3(x+4)
60-x = 3x+12
48 = 4x
x = 12

ANSWERS: The daughter's age is x=12; the mother's age is 56-x = 44

A different possible setup....

let x = daughter's age in 4 years
then 3x = mother's age in 4 years

The sum of their ages in 4 years will be 56+4+4 = 64:

x+3x = 64
4x = 64
x = 16

ANSWERS: the daughter's age is x-4 = 16-4 = 12; the mother's age now is 3x-4 = 48-4 = 44

Note that the algebra needed to solve the problem is easier with this alternative setup....

The lesson is that you should always be open to the possibility of setting up a problem in different ways.