The sum of the two numbers is 56. If the first number is by 20%, and the second is reduced by 50%

The sum of the two numbers is 56. If the first number is by 20%, and the second is reduced by 50%, then the sum of the new numbers will be 42. Find the original numbers.

The sum of the numbers x and y is 56, that is, x + y = 56. Then, according to the condition, one more equation can be drawn up: 1.2x + 0.5y = 42. The result is a system of two equations with two unknowns. Let us express x from the first equation and substitute it into the second equation: x = 56 – y,
1.2 (56 – y) + 0.5y = 42 → 67.2 – 1.2y + 0.5y = 42 → 67.2 – 42 = 1.2y – 0.5y,
25.2 = 0.7y → y = 25.2 / 0.7 → y = 36.
x = 56 – 36 = 20.
Answer: these are numbers 20 and 36.