the sum of two numbers is 18. if twice the smallest number is 6 more than the larger, find the two numbers.

Question

the equation should be in the system of linear equations.

Answer 1

Dear Kelly,

     First, write the equation out and underline all key words and numbers.

 

          add                        = 18            2X                                 =    Y +6

The sum of two numbers is 18.  If twice the smaller number is 6 more than the larger, find the two numbers.

 

Let "X" = the smaller number.    Then "Y" =larger number.

 

Given:  2X=Y +6             and      X+Y =18

 

Rewrite the first equation, so that you have 2X-6=Y.

 

Now, you can set up the two equations as a system:

 

                                                 X+Y=18

                                               2X-Y =6        Just add the two equations together to get rid of "Y."

                                                  3X=24        Divide both sides by the number next to "X."

                                                    X=24/3  =8

You might want to choose the 2X-Y=6 to solve for "Y" now.  Substitute X=8 and finish the problem.  Please check your answers into the original equations in the system of equations to see if they work.

 

I hope that I helped you.  If I did, please give me a thumbs up.

 

                                                                    Susan C. 

 

Answer 2

Hi Kelly,

 

Get used to the idea of letting variables represent the unknowns. You can use X and Y or L and S.

 

Let L= larger of two numbers; S=smaller of two numbers.

Sum of the numbers is 18, so...

L+S = 18

 

That is the first equation.

 

Twice the smallest number is 2S. But that IS 6 more than the larger. Translated into Algebra we have...

2S = 6 + L => -L + 2S = 6.

 

To solve the system it looks like the addition method will be a good choice:

 

1) L+ S = 18

2) -L +2S = 6

---------------------

3S = 24

S=8

 

If S=8, then L=10.

 

Check: the sum is 18. and twice the smallest (16) is indeed 6 more than 10.

 

Doug

Answer 3

You probably haven't studied systems of equations yet, so I'll do this with a key or legend.

 

The first thing that you must realize is that if the sum is 18, then if you know one of them, you can figure out the other number by subtracting it from 18.....for example if one number is 2, the other number is 18-2 or 16. In terms of algebra, you can make the following key:

 

smaller number is x

larger number is 18 - x

 

Now you can use this to represent the second sentence

twice the smaller is 6 more than the larger can translate to

2*     (x)            = 6+                (18-x)

2x                     = 24-x

+x                            +x

3x                     = 24

x                       = 8

 

Now plug it into the key to find that the larger is 18-8 = 10

 

So your numbers are 8 and 10.

 

You can check in the actual word problem. The sum IS 18 and twice the smaller is 16, which IS 6 more than the larger.

 

Hope this helped.