10. (a) Write 18 : 42 as a ratio in its simplest form - OCR - GCSE Maths - Question 10 - 2023 - Paper 3

Given that 1/5 of the sweets are green, if we let the total number of sweets be x, then the number of green sweets is:

$\frac{x}{5}$

The number of red sweets will be:

$x - \frac{x}{5} = \frac{5x - x}{5} = \frac{4x}{5}$

The ratio of the number of green sweets to red sweets can now be expressed as:

$\frac{\frac{x}{5}}{\frac{4x}{5}} = \frac{1}{4}$

So, in the form 1:n, we have n = 4.

If 3 machines can complete the order in 25 days, then the total work done can be calculated in machine-days:

$3 \text{ machines} \times 25 \text{ days} = 75 \text{ machine-days}$

To find the number of machines (m) needed to complete the same amount of work in 15 days, we can set up the equation:

$m \times 15 = 75$

Solving for m gives:

$m = \frac{75}{15} = 5 \text{ machines}$

Therefore, 5 machines are needed to complete the order in 15 days.