Ratios question involving 3 factors

Question

An Alloy A contains copper and tin in a ratio of 3:5 by weight . Another alloy B contains tin and zinc in the ratio of 3:7 by weight . Find the ratio of copper : tin : Zin in a new alloy containing equal weights of alloys A and B .

My attempt .

Copper : Tin = $ 3 : 5 $

Tin : Zinc = $ 3 : 7 $

I tried to make the tin ratio the same .

$ 5 X 3/5 = 3 $

Then use $ 3/5 $ and multiply the copper in alloy A .

$ 3 X 3/5 = 1.8 $

This is give me

Copper : Tin : Zinc = $ 1.8 : 3 : 7 = 9 : 15 : 35 $

However my answer is wrong . Can I get help on why ? Thanks !

Take 80 pounds of the AB compound and try to evaluate the weight of the components. Than divide the weights by their GCD. — N74, May 08 '16 at 09:51

score 1 · Answer 1 · answered Feb 01 '17 at 16:04

${{Cu}:{Sn}}={3\over5}$

${{Sn}:{Zn}}={3\over7}$

Since $Sn$ is common in both, configure the equations such that its value is the same in both. To do so, find the LCM of both values. Here, it is $15$.

So:

${{Cu}:{Sn}}={9\over15}$

${{Sn}:{Zn}}={15\over35}$

Therefore,

$Cu:Sn:Zn=9:15:35$

Ratios question involving 3 factors

1 Answers1