SOLUTION: Anna is 12 years older than her sister Sue.7 years from now Sue will be 5/9 as old as Anna.How old is Anna ? How old is She?

Question 1181704: Anna is 12 years older than her sister Sue.7 years from now Sue will be 5/9 as old as Anna.How old is Anna ? How old is She?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A typical setup for solving using formal algebra....

The number we are looking for is Anna's age, so

let x = Anna's age now
then x-12 = Sue's age now

In 7 years, Sue's age will be 5/9 of Anna's age:
x+7 = Anna's age 7 years from now
(x-12)+7 = x-5 = Sue's age 7 years from now

ANSWER: Anna is 20 years old.

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Here is an informal solution that uses "nicer" numbers....

In 7 years, Sue will be 5/9 of Anna's age, so let their ages then be 5x and 9x. The difference between their ages will be 9x-5x=4x.
But the difference in their ages is 12 years. So 4x=12; x=3.
So in 7 years their ages will be 5x=15 and 9x=27.
So Anna's current age is 27-7 = 20.

Here is the formal algebraic solution by that path....

Let 5x = Sue's age 7 years from now
let 9x = Anna's age 7 years from now

The difference in their ages then will be 4x.

The difference in their ages then, as always, is 12 years:

Anna's current age is 9x-7 = 9(3)-7 = 27-7 = 20.

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The numbers you have to work with are much easier with that method than with the method shown earlier.

It is a lesson in how there can be a great deal of difference in the amount of work you need to do to solve a problem because of different ways of setting up the problem.

Always look for possible different ways to solve problems to find ways that are easier for you.

Given the "5/9 as old..." in the statement of the problem, I would never set up the problem by the "straightforward" method that leads to having to solve an equation like , because I know there is another path that is going to be easier.

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