Answer:
Colin gets [tex]\frac{2}{9}[/tex] of the total money
Step-by-step explanation:
If we let the total amount be "90" (or any multiple of 9), then the solution gets much easy.
Let total money be 90.
Caroline gets 1/9, so that is:
1/9 * 90 = 10
Remaining is 90 - 10 = 80
This 80 is divided in the ratio 1:3, that means Colin gets 1 part and Sarah gets 3 part. That is 1 + 3 = 4 parts altogether.
80 divided in 4 parts is 80/4 = 20 each part.
Colin gets 1 part, that is 1 * 20 = 20
Colin gets 20 OUT OF 90 (total initial).
What proportion is that? We simply divide and reduce!!
20/90 = 2/9
Colin gets [tex]\frac{2}{9}[/tex] of the total money
The proportion that Colin's get from the share is 2 / 9 x
Proportion says that two ratios (or fractions) are equal.
Therefore,
let the total money they share = x
Hence,
Caroline money = 1 / 9 x
Colin and Sarah share the rest in the ratio 1:3.
Therefore,
Collin share = 1 / 4 × (x - 1 / 9 x) = 1 / 4 × 9x - x/ 9 = 1 / 4 × 8 / 9 x
Collin's share = 1 / 4 × 8 / 9 x = 8 / 36 x = 2 / 9 x
learn more on proportion here: https://brainly.com/question/14213714
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