A student spends 1/3 of his pocket money on novels, half of it on refreshments and saves ¾ of the remainder. Which amounts to N20. How much is his money?
total amount he has ---- x
amount spent = (1/3)x + (1/2)x = (5/6)x
leaving him with (1/6)x
He saves (3/4) of (1/6)x = (1/8)x
so (1/8)x = 20
x = 160
Yes
Why did you get 160
To find out how much money the student has, we need to work backwards from the given information.
Let's assume the student's total pocket money is X.
According to the given information:
1/3 of his pocket money is spent on novels,
1/2 is spent on refreshments, and
3/4 of the remainder is saved, which amounts to N20.
So, let's break it down step by step:
1. The student spends 1/3 of his pocket money on novels.
This means X * (1/3) = X/3 is spent on novels.
2. The student spends half of his pocket money on refreshments.
This means X * (1/2) = X/2 is spent on refreshments.
3. The remainder after spending on novels and refreshments is:
X - (X/3) - (X/2) = X - (2X/6) - (3X/6) = X - (5X/6)
4. The student saves 3/4 of the remainder, which amounts to N20.
Therefore, (3/4) * (X - (5X/6)) = 20
Now, let's solve the equation to find the value of X:
(3/4) * (X - (5X/6)) = 20
(3/4) * (6X/6 - 5X/6) = 20
(3/4) * (X/6) = 20
(3/4) * X = 120
3X/4 = 120
3X = 4 * 120
3X = 480
X = 480 / 3
X = 160
Therefore, the student's total pocket money is N160.