Question

A man spent 1/4 of his monthly on rent 2/5 on food and 1/6 on books. If he still had 55,000 Ghana cedis left, what was his monthly salary?​

Answer 1

$300 000

Explanation:

you want to find the remaining fraction of his money that had not been spent. that can be done by adding the spent fractions and then subtracting the sum from 1. let's add first:

`(1)/(4) + (2)/(5) + (1)/(6)`

we have to find a common denominator for each and the smallest number that satisfies this is 60 (since 60 is the smallest number divisible by 4, 5 and 6). so we convert fractions to get a denominator of 60.

`(15)/(60) + (24)/(60) + (10)/(60)`

next, we can easily add the fractions to get

`(15 + 24 + 10)/(60) = (49)/(60)`

next, we subtract that from 1:

`1 - (49)/(60) = (60)/(60) - (49)/(60) = (11)/(60)`

so $55000 is 11/60 of the salary, the last step we need to do is to divide $55000 by 11/60. recall that division with fractions can be turned into multiplication if we use the reciprocal of the fraction (flip numerator and denominator).

`55000 / (11)/(60) = 55000 * (60)/(11)`

next, notice that 11 can be cancelled out with 55000 and we get 5000, finally we have

`5000 * 60 = 300000`

as our salary.