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?
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: 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 + $ 5 w ................Equation(1) ............................................................................... 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 − $ 10 w ...............Equation(2) .............................................................................. The count of weeks when both savings are equal is defined by the model: Equation(1) = Equation(2) 60 + 5 w = 135 − 10 w
← 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
→ . 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
