Number problem

## 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?

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# 2 Answers

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

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!