One alloy contains 40% copper, while the other contains 60%. How many kilograms of each alloy do you need

One alloy contains 40% copper, while the other contains 60%. How many kilograms of each alloy do you need to take to get 70 kg of a new alloy, in which copper is 45%?

Let a be the weight of the first (40%) alloy. Then there will be 0.4x pure copper in it (40% = 0.4).

Since the new alloy has a weight of 70 kg, the weight of the second (60%) alloy is (70 – x) kg. Then pure copper in it will be 0.6 (70 – x), since 60% = 0.6.

Pure copper in the resulting alloy: 0.45 * 70 (45% = 0.45).

Let’s make the equation:

0.4x + 0.6 (70 – x) = 0.45 * 70.

0.4x + 42 – 0.6x = 31.5.

-0.2x = 31.5 – 42.

-0.2x = -10.5.

0.2x = 10.5.

x = 10.5: 0.2 = 105: 2 = 52.2 (kg) – the weight of the first 40% alloy.

70 – 52.5 = 17.5 (kg) – the weight of the second 60% alloy.