One number is 6 times larger than the other. If you subtract 80 from the larger number and add 70

One number is 6 times larger than the other. If you subtract 80 from the larger number and add 70 to the smaller number, then the results will be equal, find the sum of these numbers.

Let’s denote the lesser of the two given numbers by x.

Let us express the second number in terms of x.

The problem statement says that one of these numbers is 6 times larger than the other, therefore, the larger of the two given numbers is 6x.

Also in the condition of the problem it is said that if you subtract 80 from the larger number and add 70 to the smaller number, then the results will be equal, therefore, we can draw up the following equation:

6x – 80 = x + 70.

We solve the resulting equation:

6x – x = 80 + 70;

5x = 150;

x = 150/5;

x = 30.

Find the second number:

6x = 6 * 30 = 180.

We find the sum of these numbers:

30 + 180 = 210.

Answer: the sum of these numbers is 210.