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 us the ratio of white:milk:dark?

Answer 1

white : milk : dark

w : m : d

The ratio of white to not white is 3:4

w : (m+d) = 3:4

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

(w+m) : d = 17:4

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We treat the colons as fraction bars and cross multiply.

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

4w + 4m = 17 d

Subtracting,

4m = 17d - (3m+3d) = 14d - 3m

7m = 14 d

m/d = 14/7

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

Answer: 9:8:4

Check:

white to non white 9 to 8+4=12 = 3:4, good

non dark to dark (9+8):4=17:4, good