Expert: John Zalewski - 11/7/2011

Question
Alan spent 4/9 of his money. If he had £65 left, how much had he first.... please help me to understand on how to solve this type of question

Answer
Hello, Peter.

If Alan has 65 lira after spending 4/9 of his money, that means that he still has 5/9 of his money remaining.

So, to solve this problem divide 65 by 5/9.

65/5/9 = 65 x 9/5, or 117 lira.


Think of it this way: If you start with the amount Alan has, and you're told what fraction he spends, then you simply multiply by that fraction to find what amount of money he spent. Then subtract that amount from his original amount of money to find his current total.

(e.g., 117 lira x 4/9 = 52 lira; 117 - 52 = 65 lira.)

Because you're working backwards, and know his final money total, you divide instead of multiply. You divide by 5/9 because that is the amount he has remaining---and dividing by this amount will get you to his original amount.

Hope this helps.

Regards,
John