# Half the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.

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Expert Answers

justaguide | Certified Educator

Let the two numbers be x and y. Half the difference between two numbers is 2, (x - y)/2 = 2 = x - y = 4

The sum of the greater number and twice the smaller number is 13. This gives x + 2*y = 13

Substitute x = 4 + y in x + 2y = 13

=> 4 + y + 2y = 13

=> 3y = 9

=> y = 3

x = 7

**The two numbers are 3 and 7.**

Student Comments

eagudelo | Student

Let's say x=the greater number, and y=the smaller number.

So you have:

* x-y=z

* z/2=2

* x+2y=13.

Solve for z.

z/2=2

z=4

Plug in 4 for z.

x-y=4

Then do this:

x-y=4

x=4+y

x+2y=13

(4+y)+2y=13

3y=9

y=3

Plug in 3 for y.

x-y=4

x-3=4

x=7

So, x=7 and y=3

I hope this helps!