Final answer:
Martin and Nikita's money is shared in a 3:7 ratio, with Nikita getting £200 more than Martin. By denoting the ratio with 'x', the equation 4x = £200 is used to find that each 'x' is £50, concluding that they shared a total of £500.
Step-by-step explanation:
The question involves solving a problem based on ratios and algebra. Martin and Nikita share money in a ratio of 3:7, and Nikita receives £200 more than Martin.
To solve this, let's denote the total amount of money they shared as 'T'.
Let 'x' be the amount that represents each part of the ratio.
Therefore, Martin's share is 3x and Nikita's share is 7x.
Given that Nikita receives £200 more than Martin, we can set up the following equation: 7x - 3x = £200 which simplifies to 4x = £200.
Solving for x gives us x = £50.
Since Martin's share is 3x and Nikita's is 7x, we calculate these as follows:
Martin's share: 3x = 3(£50) = £150
Nikita's share: 7x = 7(£50) = £350
Total money shared: 3x + 7x = 10x
= 10(£50)
= £500.
Therefore, Martin and Nikita shared a total of £500.