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**Prove It** For every kg of mixture X, the ingredients are in the ratio 1 : 4 : 7, so mixture X consists of (1/12)kg of A, (4/12)kg of B, and (7/12)kg of C.

For every kg of mixture Y, the ingredients are in the ratio 2 : 5 : 8, so mixture Y consists of (2/15)kg of A, (5/15)kg of B, and (8/15)kg of C.

Therefore, when the two mixtures are added together, every 2kg of mixture X + Y will have

(1/12)kg + (2/15)kg of mixture A

= (5/60)kg + (8/60)kg of mixture A

= (13/60)kg of mixture A.

(4/12)kg + (5/15)kg of mixture B

= (20/60)kg + (20/60)kg of mixture B

= (40/60)kg of mixture B.

(7/12)kg + (8/15)kg of mixture C

= (35/60)kg + (32/60)kg of mixture C

= (67/60)kg of mixture C.

But this is for every 2kg of mixture X + Y. For every 1kg, we will need to halve each of the results.

So in every kg of X + Y, there will be (13/120)kg of A, (40/120)kg of B, (67/120)kg of C.

Therefore the ratio of A : B : C in the combined mixture is 13 : 40 : 67.