GCSE Maths change in ratio

Hello, does anyone know the method for a question along the lines of “there are pigs and sheep in the ratio 5:7, 6 of each are removed and the ratio is now 4:11, how many were there originally”? Numbers completely made up off the top of my head! I just don’t know what to do with this type of question?

Reply 1

mqb2766

21

Original post by NiseyW

Hello, does anyone know the method for a question along the lines of “there are pigs and sheep in the ratio 5:7, 6 of each are removed and the ratio is now 4:11, how many were there originally”? Numbers completely made up off the top of my head! I just don’t know what to do with this type of question?

Its usually a case of setting up a couple of (simultaneous) equations involving the original totals so P and S. Original ratio gives
P/S = 5/7
and the second ratio gives
(P-6)/(S-6) = 4/11
so just rearrange each of them and get two linear simultaneous equations and solve.

Reply 2

NiseyW

OP

10

This is an example of the type of question I need help with?

Reply 3

mqb2766

21

Original post by NiseyW

This is an example of the type of question I need help with?

Have you tried what was suggested in the ptevious post?

Reply 4

Emma_rose4014

5

Original post by NiseyW

Hello, does anyone know the method for a question along the lines of “there are pigs and sheep in the ratio 5:7, 6 of each are removed and the ratio is now 4:11, how many were there originally”? Numbers completely made up off the top of my head! I just don’t know what to do with this type of question?

I hope it is clear,
Let's say there were originally 5x pigs and 7x sheep.
After removing 6 of each, we have 5x−6 pigs and 7x−6 sheep.
The ratio of pigs to sheep after removal is 4:11. So, we can write the equation: 5x-6/7x-6 = 4/11
To solve this equation, we will simply cross multiply: 11(5x−6)=4(7x−6)
= 55x−66=28x−24
Now we will solve for x: 55x−28x=66−24
= 27x=42
= x=42/27
= 14/9
x represents the ratio between pigs and sheep, which must be a whole number, we need to find a common multiple of 5 and 7 which would be 35
let x=35,
Number of pigs = 5×35=175
Number of sheep= 7x35=245

GCSE Maths change in ratio

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