Final answer:
Carley and James share money in a 5:3 ratio with James receiving £70 more. Solving the problem with algebra, one part of the ratio is found to be worth £35. Multiplying by Carley's share of the ratio (5 parts), we conclude that Carley gets £175.
Step-by-step explanation:
To solve the problem where Carley and James share money in the ratio 5:3 and James gets £70 more, we need to work out the total amount of money shared and then calculate Carley's share.
Let's let the amount that represents one part in the ratio be 'x'. If Carley has 5 parts and James 3 parts with James getting £70 more, we can write two expressions for their shares:
- Carley's share = 5x
- James' share = 3x + £70
Since we know that James gets £70 more than what the ratio suggests (3x), we can equate Carley's share to James' share plus £70:
5x = 3x + £70
Subtracting 3x from both sides gives us:
2x = £70
Dividing both sides by 2:
x = £35
This means that one part of the ratio is worth £35. To find out how much Carley gets, we multiply this by her share of the ratio:
Carley's share = 5x = 5 × £35 = £175
Therefore, Carley receives £175.