0
$\begingroup$

I was asked by s student to solve this question based on ration proportion and my answer was 5:1 although not sure. The question was, The ratio of goats to sheep is 4:3.sheep to cows 5:2.cows to donkeys 3:2. Find the ratio of g:d? Kindly,is it correct?

$\endgroup$
1
$\begingroup$

If you want an answer that rehearses the logic behind why you can just multiply the ratios that stays in the integers, here is such an answer:

For every 2 donkeys, you have 3 cows. For every 2 cows, you have 5 sheep. So for every 6 cows you have 15 sheep, or 4 donkeys. For every 3 sheep you have 4 goats, so for 15 sheep (or 4 donkeys, or 6 cows) you have 20 goats.

So, we've shown that for every 20 goats you have 4 donkeys, so for every 5 goats you have 1 donkey, so goats, donkeys are in ratio 5:1.

You can generalise this argument to persuade yourself that you can always just multiply the ratios A:B, B:C to get to ratio A:C, or indeed that $$A_1:A_n=(A_1:A_2 )\times (A_2:A_3) \times \cdots \times (A_{n-1}:A_n)$$

$\endgroup$
  • $\begingroup$ Thanks for clarification $\endgroup$ – Makau Elijah Nov 6 '18 at 17:04
1
$\begingroup$

Because $$g:d=\frac{g}{s}\cdot\frac{s}{c}\cdot\frac{c}{d}=\frac{4}{3}\cdot\frac{5}{2}\cdot\frac{3}{2}=5=5:1.$$

$\endgroup$
  • $\begingroup$ Thanks for clarification $\endgroup$ – Makau Elijah Nov 6 '18 at 17:03
  • $\begingroup$ You are welcome! $\endgroup$ – Michael Rozenberg Nov 6 '18 at 17:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.