The sum of two numbers is 26. the larger of the two numbers is 14 more than three times the smaller number. what are the two numbers?

Question

Number problem

Answer 1

x=smaller #

y=larger #

x+y=26

y=3x+14

x+(3x+14)=26

4x+14=26

4x=12

x=3

y=3(3)+14

y=9+14

y=23

answer: 3 and 23

Answer 2

Hi Again Roseland;

Another great question!  I appreciate it!

x=smaller number

y=larger number

 

x+y=26

y=3x+14

 

We need to perform a method called SUBSTITUTION.  I will illustrate.

Let's begin with the first equation, because it is easiest.

Let's isolate for y...

x+y=26

y=26-x

 

Now...

26-x=3x+14

 

Let's combine like terms...

Let's add x to both sides...

x+26-x=3x+14+x

26=4x+14

Let's subtract 14 from both sides...

-14+26=4x+14-14

12=4x

Let's divide both sides by 4...

12/4=(4x)/4

 

x=3

y=26-3=23

 

Let's check our results...

Does y=3x+14

23 ???  3(3)+14

23  ??? 9+14

23=23

Yes!