Find two numbers, if their sum is − 1/3 and their difference is 18

Question

Find two numbers, if their sum is − 1/3 and their difference is 18

Answer 1

Let's call the two unknown numbers x and y. According to the problem:

x + y = -1/3

x - y = 18

There are several different ways to do this problem. Since it sets up so nicely with a positive y in one and a negative y in the other, I'm going to just add the two problems together.

x + x = 2x y - y cancels out -1/3 + 18 = 17 2/3

So now you have one equation: 2x = 17 2/3

In order to get x by itself, you divide both sides of the equation by 2. It's easier to multiply an improper fraction than a mixed number, so I'm going to turn 17 2/3 into 51/3.

2x/2 = x

51/3 / 2 is the same as 51/3 x 1/2. Multiply across the top to get 51. Multiply across the bottom to get 6.

51/6 = 8 3/6, which reduces to 8 1/2.

Now we know one of the numbers is 8 1/2. We can plug into either equation to find out the other number.

x + y = -1/3

8 1/2 + y = -1/3

Subtract 8 1/2 from both sides: y = -1/3 - 8 1/2.

Let's turn 8 1/2 back into an improper fraction. 17/2.

-1/3 - 17/2. In order to subtract fractions, you have to have the same denominator. Let's change both fractions to something with a denominator of 6.

-1/3 x 2/2 = -2/6

17/2 x 3/3 = 51/6.

-2/6 - 51/6 = -53/6

Finally, we turn that back into a mixed number: - 53/6 = -8 5/6

So your two numbers are 8 1/2 and -8 5/6