Question

I have a box of chocolates with white,milk and dark chocolate in. The ratio of white to not white is 3:4. The ratio of not dark to dark is 17:4. What is the ratio of white:milk:dark

Answer 1

The ratio of white:milk:dark is 9:8:4

Explantion:

Let w represent white chocolate , m represent milk chocolate and d represent dark chocolate

The ratio of white to not white is 3:4

Here not white means , it can be milk or dark chocolate

Then

w : (m+d) = 3:4 -----------------------------(1)

The ratio of not dark to dark is 17:4.

Again not dark means , it will be white or milk chocolate

Then,

(w+m) : d = 17:4 -----------------------------(2)

Representing (1) in fractions

`(w)/(m+d) =(3)/(4)`

4w = 3(m+d)

4w = 3m +3d

4w -3m =3d------------------------------(3)

Representing (2) in fractions

`((w+m))/(d)= (17)/(4)`

4(w+m) = 17d

4w +4m = 17d---------------------------(4)

Subtracting (3) from (4)

4w +4m = 17d

4w -3m = 3d

(-)

-------------------------------

7m = 14d

-------------------------------

`(m)/(d) = (14)/(7)`

`(m)/(d) = (2)/(1)`

m:d = 2:1

Since w:(m+d)=3:4 let's make m:d a multiple of 4.

m:d = 8:4

w : (m+d) = 3:4 = 9:12

w:m:d = 9:8:4