Question

Daniel wants to share some money between three different charities. He splits £430 into three amounts that he calls A, B and C.

The ratio A: B is 2:7.
The ratio A: Cis 3: 8.
Work out how much money
C
represents.

Answer 1

To work out how much money C represents, convert the given ratios into a single ratio that includes A, B, and C. The combined ratio A:B:C is 6:21:16, from which we establish each part is worth £10. Multiplying the value associated with C in the ratio (16) by £10 gives us £160 for C.

Step-by-step explanation:

The task is to find out how much money C represents from the total sum of £430, given the ratios A:B as 2:7 and A:C as 3:8. To solve this, let's find a common multiple for A in both ratios to represent it as a single value we can use to define a composite ratio. This composite ratio will include all three amounts, A, B, and C.

We can write the ratios as fractions:

• A/B = 2/7
• A/C = 3/8

To find a common value for A, we need a common multiple of 2 and 3. The smallest common multiple is 6. Now we can write new ratios multiplying them to have A as 6:

• For A:B -> 2:7, multiplying by 3 gives us A:B as 6:21,
• For A:C -> 3:8, multiplying by 2 gives us A:C as 6:16.

Now, combining these we have the full ratio A:B:C as 6:21:16. The sum of the parts of the ratio is 6 + 21 + 16 = 43. Since the total amount of money is £430, each part of the ratio is worth £430 ÷ 43 = £10.

To find C, we multiply the ratio part for C (16) by the value of each part (£10): C = 16 × £10 = £160.

Therefore, the amount represented by C is £160.