The alloy consists of zinc and copper, included in it in a ratio of 1: 2, and the other alloy contains the same metals

The alloy consists of zinc and copper, included in it in a ratio of 1: 2, and the other alloy contains the same metals, but in a ratio of 2: 3. How many parts of each of these alloys do you need to take to get 3 alloy containing zinc and copper in a ratio of 17:27?

The first salv contains 1 part zinc and 2 parts copper. Let one part be equal to x, then zinc in the first alloy is x, and copper is 2x.

The second alloy contains 2 parts of zinc (let it be 2y), and 3 parts of copper in it (3y).

We get the third alloy: zinc in it will be (x + 2y), and copper will be (2x + 3y).

Since the ratio will be 17/27, we make up the proportion.

(x + 2y) / (2x + 3y) = 17/27.

17 (2x + 3y) = 27 (x + 2y).

34x + 51y = 27x + 54y.

34x – 27x = 54y – 51y.

7x = 3y.

x / y = 3/7.

In the first alloy there were 3 parts (which we designated as x), that is, we will take 3 parts x for the new alloy, in the second alloy 2y + 3y = 5y, five parts y.

That is, 3x / 5y = (3 * 3) / (5 * 7) = 9/35.

The answer is 9 to 35.