pat spent 50% of his money in one shop and 25% of what was left in another shop.he had £12 left. what fraction of his money had he left and how much had he at first.
amount spent in second shop = (1/4)(1/2) = 1/8
so in both he spent: 1/2 + 1/8 = 5/8
leaving him with 3/8
3/8 x = 12
x = 32
He started with £32
check:
he spent 1/2 is 1st store leaving him with 16
he spent 1/4 of that or 4 in the 2nd store.
That leaves him with 16-4 = 12
To find out the fraction of Pat's money he had left, we need to work backward from the information given.
Let's start with the amount he had left, which is £12. This represents 100% minus the percentages he spent in the two shops.
So if £12 represents 100% of his money, we can set up the following equation:
100% - (50% + 25%) = £12
To add the percentages, we need to convert them into decimal form. 50% is equal to 0.50, and 25% is equal to 0.25. Plugging these values into the equation, we get:
100% - (0.50 + 0.25) = £12
Simplifying further:
100% - 0.75 = £12
At this point, we can convert 100% into a decimal by dividing it by 100, which gives us 1.0.
1.0 - 0.75 = £12
0.25 = £12
Now, to find out how much Pat had at first, we divide £12 by 0.25:
£12 ÷ 0.25 = £48
So Pat initially had £48.
To find the fraction of his money that he had left, we divide the amount he had left by the amount he initially had:
£12 ÷ £48 = 1/4
Therefore, Pat had 1/4 (or 25%) of his money left.