Olivia and Jessica have in total half as many sweets as Fran and Gary have in total - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 3

Let the total number of sweets that Olivia and Jessica have be represented as:

If Olivia has 9m sweets and Jessica has 1m sweets, then:

$ext{Total sweets for Olivia and Jessica} = 9m + 1m = 10m$

According to the problem, Olivia and Jessica have half as many sweets as Fran and Gary, thus:

10m = rac{1}{2}(5k)
which simplifies to: 10m = rac{5k}{2}
Multiplying both sides by 2 gives: $20m = 5k$
Therefore, we have: $k = 4m$

Now, substituting $k$ back into the expressions for sweets:

• Fran: $w = 2k = 2(4m) = 8m$
• Gary: $x = 3k = 3(4m) = 12m$
• Olivia: $y = 9m$
• Jessica: $z = 1m$

Thus, the ratio is: $w:x:y:z = 8m:12m:9m:1m$

To simplify this ratio: $8:12:9:1$