# 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?

Nov 10, 2016

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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$\textcolor{b l u e}{\text{Using first principle method}}$

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) .............................................................................. 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 $10 w$to both sides $60 + 5 w + 10 w = 135$Subtract 60 from both sides $5 w + 10 w = 135 - 60$Simplify $15 w = 75$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 = \frac{75}{15} \to \frac{75 \div 15}{15 \div 15} = \frac{5}{1} = 5$$w = 5\$