Question 1181704
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A typical setup for solving using formal algebra....<br>
The number we are looking for is Anna's age, so<br>
let x = Anna's age now
then x-12 = Sue's age now<br>
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<br>
{{{x-5 = (5/9)(x+7)}}}
{{{9(x-5) = 5(x+7)}}}
{{{9x-45 = 5x+35}}}
{{{4x = 80}}}
{{{x = 20}}}<br>
ANSWER: Anna is 20 years old.<br>
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Here is an informal solution that uses "nicer" numbers....<br>
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.<br>
Here is the formal algebraic solution by that path....<br>
Let 5x = Sue's age 7 years from now
let 9x = Anna's age 7 years from now<br>
The difference in their ages then will be 4x.<br>
The difference in their ages then, as always, is 12 years:<br>
{{{4x=12}}}
{{{x=3}}}<br>
Anna's current age is 9x-7 = 9(3)-7 = 27-7 = 20.<br>
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The numbers you have to work with are much easier with that method than with the method shown earlier.<br>
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.<br>
Always look for possible different ways to solve problems to find ways that are easier for you.<br>
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 {{{x-5 = (5/9)(x+7)}}}, because I know there is another path that is going to be easier.<br>