Question 1204027
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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.<br>
Probably the standard approach...<br>
let x = daughter's age
then 56-x = mother's age (the sum of their ages is 56)<br>
x+4 = daughter's age in 4 years
(56-x)+4 = 60-x = mother's age in 4 years<br>
In 4 years, the mother's age will be 3 times the daughter's age:<br>
60-x = 3(x+4)
60-x = 3x+12
48 = 4x
x = 12<br>
ANSWERS: The daughter's age is x=12; the mother's age is 56-x = 44<br>
A different possible setup....<br>
let x = daughter's age in 4 years
then 3x = mother's age in 4 years<br>
The sum of their ages in 4 years will be 56+4+4 = 64:<br>
x+3x = 64
4x = 64
x = 16<br>
ANSWERS: the daughter's age is x-4 = 16-4 = 12; the mother's age now is 3x-4 = 48-4 = 44<br>
Note that the algebra needed to solve the problem is easier with this alternative setup....<br>
The lesson is that you should always be open to the possibility of setting up a problem in different ways.<br>