Answer:
Suppose that the family's monthly income is X.
we know that they spend:
(3/7)*X on food.
(5/14)*X on clothing
(1/5)*X on rent.
a) what fraction of the family's income is spent in other things?
To solve this, we assume that N is spent on other things, then we should have that:
(3/7)*X + (5/14)*X + (1/5)*X + N*X = X
We can divide both sides by X to remove it, so we get:
(3/7) + (5/14) + (1/5) + N = 1
we can solve this for N.
3/7 + 5/14 + 1/5 + N = 1
6/14 + 5/14 + 1/5 + N = 1
(6 + 5)/14 + 1/5 + N = 1
11/14 + 1/5 + N = 1
The smallest common factor of 14 and 5 is 14*5 = 70
Then we need to multiply the first fraction by (5/5) and the second by (14/14)
(5/5)*(11/14) + (14/14)*(1/5) + N = 1
55/70 + 14/70 + N = 1
69/70 + N = 1
N = 1 - 69/70 = 1/70
N = 1/70
This means that they spent 1/70 of their monthly income on other things.
b) One particular month, the family spends GH¢2,400 on other things, then if the monthly income is X, we have:
(1/70)*X = GH¢2,400
X = 70* GH¢2,400 = GH¢168,000
This means that the monthly income of the family is GH¢168,000
And we know that they spend (5/14)*X on clothing, then this month they spent:
(5/14)*GH¢168,000 = GH¢60,000 on clothing.
