# Currently, you have $60 and your sister has $135 You decide to save $5 of your allowance each week, while your sister decides to spend her whole allowance plus $10 each week. How long will it be before you have as much money as your sister?

##### 1 Answer

It will take 5 weeks for both to have the same amount of savings.

It takes a lot longer to explain what is going on than to do the actual maths with shortcuts.

#### Explanation:

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Let the count of weeks be

You start off with $60 in your savings

This is increased by $5 each week so the total in your savings at any given count of weeks count is:

...............................................................................

Your sister does not add to her savings but reduces it by $10 each week. So her savings at any given week count is:

..............................................................................

The count of weeks when both savings are equal is defined by the model:

Equation(1) = Equation(2)

Add

Subtract 60 from both sides

Simplify

Divide both sides by 15

Did you know you can treat units of measurement ($) the same way you do the numbers.

The $ signs cancel out so you are only left with numbers