Question

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?

Answer 1

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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`color(blue)("Using first principle method")`

Let the count of weeks be `w`

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:

`$60+$5w`................Equation(1)
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Your sister does not add to her savings but reduces it by $10 each week. So her savings at any given week count is:

`$135-$10w`...............Equation(2)
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The count of weeks when both savings are equal is defined by the model:

Equation(1) = Equation(2)

`60+5w=135-10w" "color(brown)(larr" in dollars")`

Add `10w` to both sides

`60+5w+10w=135`

Subtract 60 from both sides

`5w+10w=135-60`

Simplify

`15w=75`

Divide both sides by 15

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

`w=($75)/($15) " "rarr color(white)(.)75/15$/$`

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

`w=75/15 ->(75-:15)/(15-:15)=5/1=5`

`w=5`