I have some money. I spend half at the bookshop, a quarter at the supermarket and an eighth on sweets. I have £3.25 left. How much money did I have to start with?
You spent 1/2 + 1/4 + 1/8 or 7/8 of your money
leaving you with 1/8 of your money
1/8 x = 3.25
so you had x = 3.25/(1/8) = £ 26
To find out how much money you had to start with, we can work backwards from the amount you have left.
Let's assume the amount you had to start with is X.
You spent half of the money at the bookshop, which is X/2.
You spent a quarter of the money at the supermarket, which is X/4.
You spent an eighth of the money on sweets, which is X/8.
So, the total amount spent is X/2 + X/4 + X/8.
Since you have £3.25 left, we can write an equation:
X - (X/2 + X/4 + X/8) = 3.25
To solve this equation, we'll first simplify the right-hand side:
X - (X/2 + X/4 + X/8) = 3.25
X - (4X/8 + 2X/8 + X/8) = 3.25
X - (7X/8) = 3.25
Next, let's find a common denominator for X and 7X/8, which is 8:
8X/8 - (7X/8) = 3.25
(8X - 7X)/8 = 3.25
X/8 = 3.25
To isolate X, multiply both sides of the equation by 8:
8 * (X/8) = 8 * 3.25
X = 26
Therefore, you had £26 to start with.
To determine the amount of money you had to start with, we can follow these steps:
1. Subtract the remaining amount (£3.25) from the total amount spent on books, supermarket, and sweets.
Total spent = 1/2 + 1/4 + 1/8 = 7/8 (since 1/2 + 1/4 + 1/8 = 4/8 + 2/8 + 1/8 = 7/8)
Remaining amount = Total spent - £3.25
2. Find the value of 7/8 in pounds.
One pound = 8/8
£1 = 1/8
So, 7/8 of a pound = 7/8 * £1 = £7/8
3. Calculate the total amount you had to start with.
Total amount = Remaining amount + £3.25
Total amount = £7/8 + £3.25
Hence, the amount of money you had to start with can be found by adding £7/8 to £3.25.