To 4kg of gold-silver alloy, 1kg of gold was added. At the same time, the percentage of silver content in the alloy decreased

To 4kg of gold-silver alloy, 1kg of gold was added. At the same time, the percentage of silver content in the alloy decreased by 10%. How many kilograms of silver is in the alloy?

Let us express through the variable a the mass of silver contained in the original alloy.

Accordingly, we are able to represent the initial silver content in the indicated alloy through (a: 4) * 100% = 25a%.

Let’s find out the mass of the new alloy, because we know from the conditions of the assignment that a kilogram of gold was added to it:

4 + 1 = 5.

Since we know from the condition that after this manipulation the silver content dropped by ten percent, we write down the equation and find out the mass of silver:

25a – (a: 5) * 100 = 10;

25a – 20a = 10;

5a = 10;

a = 2.

Answer: 2 kg.