The first number is 22 less than the second. Find these numbers if their sum is 78.

The task is easily solved by a system of equations, since the condition contains two unknown numbers.

Let x – 1 number, then y – 2.

Let’s compose a system of equations:

y – x = 22 (since 1 number is less than 2 by 22),
y + x = 78;

Next, we express y through x and substitute it into the second equation:

y = 22 + x,
22 + x + x = 78.

We solve only the second equation:

22 + 2x = 78,

2x = 78 – 22,

2x = 56,

x = 56: 2,

x = 28.

Substitute x in the 2 equation and get y:

y + 28 = 78,

y = 78 – 28,

y = 50.

Verification:

28 + 50 = 78.

Answer: 28 and 50.