The sum of the two conceived numbers is 45. If one of them is increased by 4 times, and the other by 20

The sum of the two conceived numbers is 45. If one of them is increased by 4 times, and the other by 20, then the sum of the received numbers will be equal to 155. Find the conceived numbers.

We compose a system of equations in which we write the first number as x, and the second as y.

x + y = 45.

After x was increased 4 times, it was: 4 * x.

After increasing the number y by 20, it became equal to: y + 20.

4 * x + y + 20 = 155.

We express the number x from the first equation and substitute it into the second.

x = 45 – y.

4 * (45 – y) + y + 20 = 155.

180 – 4 * y + y + 20 = 155.

-3 * y = 155 – 200.

3 * y = 45.

y = 45/3 = 15 (second number).

x = 45 – 15 = 30 (first number).

Answer:

The numbers are 30 and 15.