The first vase had many times more flowers than the second. After 12 flowers were taken from the first vase

The first vase had many times more flowers than the second. After 12 flowers were taken from the first vase, and 8 were added to the second, the flowers became equal in both vases. How many flowers were in the second vase originally?

Let’s denote by x the number of flowers that stood in the second vase.

In the statement of the problem it is said that the first vase had 5 times more flowers than the second, therefore, the number of flowers that stood in the first vase is 5x.

It is also known that after 12 flowers were taken from the first vase, and 8 were added to the second, the flowers became equal in both vases, therefore, we can draw up the following equation:

5x – 12 = x + 8.

We solve the resulting equation:

5x – x = 12 + 8;

4x = 20;

x = 20/4;

x = 5.

We find how many flowers were in the first vase:

5x = 5 * 5 = 25.

Answer: the first vase had 25 flowers, the second vase had 5 flowers.