A number x is 4 less than three times another number y. If their sum is increased by 5, the result is 25. Find both the numbers.

Let the number y be represented as y. Then, the number x can be expressed in terms of y as:

x = 3y – 4

According to the problem, if we take the sum of x and y and increase it by 5, we get 25. This can be written as:

x + y + 5 = 25

Now, substituting the expression for x into this equation:

(3y – 4) + y + 5 = 25

Combining like terms:

4y + 1 = 25

Subtract 1 from both sides:

4y = 24

Dividing both sides by 4:

y = 6

Now that we have the value of y, we can find x:

x = 3(6) – 4

Calculating this gives:

x = 18 – 4 = 14

Therefore, the two numbers are:

x = 14 and y = 6.