Ratios

[heshamelaziry]

In a certain cake recipe, in which all quantities are measured by weight, the ratio of flour to eggs is 7:4, the ratio of eggs to sugar is 12:5, and the ratio of flour to milk is 3:2. What is the ratio of milk to sugar?

OA 14 to 5

This particular ratio problem annoys me the most. There is similar one in OG 12. I understand the explanation when I see it, but never able to apply the method myself. Any creative techniques are greatly appreciated.

[truplayer256]

F= Flour
E= Eggs
M= Milk

F/E=7/4 (1)

E/S=12/5 (2)

F/M=3/2 (3)

Divide equation 1 by equation 3 to get M/E=7/4*2/3=7/6

Reciprocate equation two to get S/E=5/12. We need to reciprocate the equation so we can do the following:

(M/E)/(S/E)=M/S=7/6*12/5=14/5

[heshamelaziry]

F= Flour
E= Eggs
M= Milk

F/E=7/4 (1)

E/S=12/5 (2)

F/M=3/2 (3)

Divide equation 1 by equation 3 to get M/E=7/4*2/3=7/6

Reciprocate equation two to get S/E=5/12. We need to reciprocate the equation so we can do the following:

(M/E)/(S/E)=M/S=7/6*12/5=14/5

How do you develop this solution logically. I see theis and I don't know where to start ?

[Abdulla]

Hesham, Here another way that worked for me best.

M : F : E : S -------------------(1)
---: 7 : 4 :---
Now go to the second ratio

M : F : E : S -------------------(2)
---:---: 12: 5

always try to find multiples, which is in this case E.

Multiply (1) by 3 to get E=12

M : F : E : S ---------------------(3)
---:21:12: 5

The last ratio given is

M : F
2 : 3

so, to fit this ratio into the ratio that we're working on, multiply the ratio by 7 ( 3*7 = 21 which is what we need ) and plug it.

M : F : E : S ---------------------(4)
14 : 21 : 12: 5

M : S
14 : 5 is the answer.