Tumtuo spent1/ 4 of his money on food 1/6 of the remaining money on sweet and spent 1/5 of what still remaining on classes. If he had GHd10. 50p left on him what is the total amount of money Tumtuo had on him
Let's work backwards to find the total amount of money Tumtuo had.
First, we know that he had GH₵10.50 left after all his spending.
Next, we need to undo the last step and add back the money he spent on classes. We know he spent 1/5 of what was still remaining at that point, so we can write an equation:
(1 - 1/4) * (1 - 1/6) * x - 1/5 * (1 - 1/4) * (1 - 1/6) * x = GH₵10.50
Simplifying the fractions on the left side:
3/4 * 5/6 * x - 1/20 * 3/4 * 5/6 * x = GH₵10.50
Multiplying the fractions:
15/24 * x - 3/480 * x = GH₵10.50
Simplifying:
5/8 * x - 1/160 * x = GH₵10.50
Combining like terms:
31/160 * x = GH₵10.50
Multiplying both sides by the reciprocal of 31/160:
x = GH₵54
So Tumtuo started with GH₵54.
Let's calculate step by step:
1. Tumtuo spent 1/4 of his money on food. So, he has 3/4 of his money remaining.
2. Tumtuo spent 1/6 of the remaining money on sweets. Therefore, he has 5/6 * 3/4 = 15/24 = 5/8 of his money remaining.
3. Tumtuo spent 1/5 of what still remains on classes. So, he has 4/5 of 5/8 = 4/5 * 5/8 = 4/8 = 1/2 of his money remaining.
4. It is given that Tumtuo has GHd10.50p left. This amount corresponds to 1/2 of his money.
Let X be the total amount of money Tumtuo had.
Therefore, 1/2 * X = GHd10.50p
To solve for X, we can multiply both sides by 2:
X = 2 * GHd10.50p
X = GHd21
Therefore, the total amount of money Tumtuo had on him was GHd21.