Help with GCSE Ratios - Where am I going wrong?

Question 16:

see attached image

My attempt:

y = 1.2x = \frac{6}{5}x \Rightarrow 6x=5y

Therefore

6 \colon 5

in the form of

x \colon y

The correct correct answer is

5 \colon 6

Question 26:

see attached image

My attempt:

b = \frac{2}{3} c \Rightarrow 3b = 2c \Rightarrow 6b = 4c

We are given

5a = 4c

I have worked out the value of

4c

so equating everything together yields:

5a = 6b = 4c

, in other words,

5 \colon 6 \colon 4

in the form of

a \colon b \colon c

.

The correct answer is

12 \colon 10 \colon 15

I understand the solutions to both questions, in fact, they seem more logical than my final answer but what is it that I am assuming which causes me to deviate from the correct answer?

Thanks

(edited 7 months ago)

Screenshot 2023-09-14 at 16.08.16.png14.5KB

Screenshot 2023-09-14 at 16.27.52.png56.6KB

Reply 1

mqb2766

For the first one, 6x=5y is good and this equality holds when x=5,y=6 and both sides = 30. Or
x/y = 5/6
Hence the ratio x:y = 5:6. Intuitively if you have one part, then x=5 and y=6, so y is 20% more.

For the second you have
a/c = 4/5
and
b/c = 2/3
so
a/b = 4/5 * 3/2 = 12/10

So a:b:c = 12 : 10 : 15

(edited 7 months ago)

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Help with GCSE Ratios - Where am I going wrong?

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