The two alloys together weigh 55kg. The first alloy contains 7 kg of copper, and the second – 5 kg of copper.

The two alloys together weigh 55kg. The first alloy contains 7 kg of copper, and the second – 5 kg of copper. How much does each of the alloys weigh if the second alloy contains 5% more copper than the first?

Let a be the mass of the first alloy and b the mass of the second alloy.

a + b = 55 (two alloys weigh 55 kg).

Let x% be the percentage of copper in the first alloy, then (x + 5)% is the percentage of copper in the second alloy.

The first alloy contains 7 kg of copper: x% of a is equal to 7 kg: (x * a) / 100 = 7; x * a = 700; x = 700 / a.

The second alloy contains 5 kg of copper: (x + 5)% of b is equal to 5 kg: (x + 5) b / 100 = 5; xb + 5b = 500; xb = 500 – 5b; x = (500 – 5b) / b.

We got two values ​​of x, let’s equate them:

700 / a = (500 – 5b) / b.

Since a + b = 55, a = 55 – b.

700 / (55 – b) = (500 – 5b) / b.

(55 – b) (500 – 5b) = 700b.

5 (55 – b) (100 – b) = 700b.

Divide by 5: (55 – b) (100 – b) = 140b.

5500 – 100b – 55b + b² – 140b = 0.

b² – 295b + 5500 = 0.

D = (-295) ² – 4 * 5500 = 65025 (√D = 255);

b1 = (295 – 255) / 2 = 20 (kg) is the mass of the second alloy.

b2 = (295 + 255) / 2 = 550 (it can’t be, two alloys weigh only 55 kg).

a = 55 – 20 = 35 (kg) is the mass of the first alloy.

Answer: 35 kg and 20 kg.