How can we find the numbers x and y if x is 4 less than three times y and their sum increases by 5 to equal 25?

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To solve the problem where we have two numbers, x and y, we can break it down into two equations based on the information given:

  1. We know that x is 4 less than three times y. This can be written as:

    2. x = 3y – 4

  2. We are also told that if we increase the sum of x and y by 5, the result is 25. This gives us another equation:

    3. x + y + 5 = 25

    If we simplify this second equation, we can rewrite it as:

    x + y = 20

Now we have a system of equations:

  • Equation 1: x = 3y – 4
  • Equation 2: x + y = 20

We can substitute x from Equation 1 into Equation 2:

(3y – 4) + y = 20

Combining like terms, we get:

4y – 4 = 20

Now, add 4 to both sides:

4y = 24

Next, divide both sides by 4:

y = 6

With the value of y found, we can substitute it back into Equation 1 to find x:

x = 3(6) – 4

Calculating this gives:

x = 18 – 4

x = 14

We have now found the values of both numbers:

x = 14 and y = 6.

In conclusion, the two numbers are 14 and 6.

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