One number is three less than three times another. If their sum is increased by six the result is nineteen. Find the numbers

Question

How to set it up 

Answer 1

Hello, Jenn.

 

Let's let "X" represent one of the numbers, and let's let "Y" represent the other number.  From the problem statement, we can form two equations.

 

                                                         X = 3Y - 3   (1)

and

                                                         X + Y + 6 = 19   (2)

 

From equation (1), we can substitute "3Y-3" for "X" in equation (2); and we get

 

                                                         3Y - 3 + Y + 6 = 19

 

Simplifying the left side of the equation, we see that 

 

                                                         4Y + 3 = 19

 

Subtracting "3" from both sides of the equation

 

                                                        4Y = 16

 

And we solve for "Y" by dividing both sides of the equation by "4"

 

                                                        Y = 4

 

Substituting "4" for "Y" in equation (1), we get

 

                                                         X = 3(4) - 3

or

                                                         X = 12 - 3 = 9

 

So, the numbers that you are looking for are 4 and 9.