5 (a) Write 12:54 as a ratio in its simplest form - OCR - GCSE Maths - Question 5 - 2018 - Paper 1

First, convert 1 kg to grams:

1 kg = 1000 g.

Now we can write the ratio as:

$$400g : 1000g = 1 : n$$

To find n, we can use the proportions that arise from simplifying:

$\frac{400}{1000} = \frac{1}{n}$

Cross-multiplying gives:

$400n = 1000$

Dividing both sides by 400:

$n = \frac{1000}{400} = 2.5$

Thus, the value of n is 2.5.

Let the total amount of money shared be represented as S. The ratio of Amanda to Wim is 2:5, which means for every 7 parts of the total amount (2 + 5 = 7), Wim takes 5 parts.

Given that Wim receives £115, we can set up the equation:

$\frac{5}{7}S = 115$

To find S, multiply both sides by 7:

$5S = 115 \times 7$

Calculating the right side:

$5S = 805$

Now divide by 5:

$S = \frac{805}{5} = 161$

Therefore, the total amount of money shared is £161.