Two numbers have a sum of fourteen. The larger number is twice the smaller number plus two. What are the two numbers?

Question

I need help with this for my homework 

Answer 1

Let's start by turning the information into equations. We have 2 variables. Let's call them x and y.

 

The first sentence tells us that x + y = 14.

The second says that y = 2x + 2.

 

Now we need to combine the two equations. There are a couple ways to do this, but I'll use substitution. The second equation tells us that y equals 2x+2, so let's substitute that into the first:

 

x + (2x + 2) = 14

 

Now, we solve for x:

 

3x + 2 = 14

3x = 12

x = 4

 

We got one of the numbers! To get the other, plug 4 in as x in one of the equations (I'll use the second):

 

y = 2(4) +2

y = 8 + 2

y = 10

 

Let's check our answers in the first equation by plugging in 4 as x and 10 as y:

 

4 + 10 = 14

 

This is correct, so our answers were right. The numbers are 4 and 10!