Final answer:
Using algebra and the given ratio of 2:4:9, it's determined that the common unit is £12, leading to Chen receiving a total of £48.
Therefore, the correct answer is Option 2.
Step-by-step explanation:
The problem involves dividing an amount of money among three people, Amanda, Chen, and Mark, based on a specified ratio and a given difference in money received by two of the individuals. To solve this, we need to represent the ratio numerically and use algebra to find the value that matches the conditions in the problem.
The ratio is given as 2:4:9. If we let the common unit be x, then Amanda receives 2x, Chen receives 4x, and Mark receives 9x. According to the given information,
Mark got £84 more than Amanda.
Algebraically, this can be written as 9x - 2x = £84.
Simplifying this equation, we get 7x = £84, which means x = £12.
Since Chen receives 4x, we multiply 4 times x (which is £12) to find out how much Chen gets:
4 * £12 = £48.
Therefore, Chen gets £48, making Option 2 the correct answer.