Question

The sum of two numbers is 51 and the difference is 9. What are the numbers?

Answer 1

So with this you'll be doing a system of equations. The first equation is to represent the sum of the numbers and the second is to represent the difference of numbers.

Let x = larger number and y = smaller number.

x + y = 51

x - y = 9

For this, I'll be using the elimination method. And to do that, all you need to do is add (x+y=51) and (x-y=9) together, and your result will be 2x = 60. From here we can solve for x.

For that equation, all you need to do is divide 2 on both sides, and your answer will be x = 30.

Now that we have x, we can substitute x for 30 in either equation to solve for y. I'll use the 1st equation.

30 + y = 51

y = 21

In short, the two numbers are 21 and 30.

Answer 2

The numbers are 30 and 21.

I find it by dividing 51 by 2, and then adding half of 9 to it.

So

51/2 = 25.5

25.5 + (9/2) = 30

51 - 30 = 21

30 - 21 = 9