What is the sum of two numbers is 111 and their difference is 17 What are the two numbers?

Answer 1

Suppose the numbers are X and Y

X + Y = 111

X - Y = 17

Add the two equations: 2X = 128

Divide by 2: X = 64

Substitute in the first equation: 64 + Y = 111

So Y = 111 - 64 = 47

We can also solve this using the substitution method.

Rewrite one of the equations in terms of either variable. I chose to write the second equation to solve for x in terms of y.

x=17+y

Now that we have a value for x, substitute that value into the first equation. It is important to substitute into the equation that we did not use to get our new expression for x.

(17+y)+y=111

Great! Now we only have one variable. Now solve for y.

17+2y=111

2y=94

y=47

Now we know that y equals 47. We can substitute that value into either equation to solve for x.

x+47=111

x=64

Now we know that x equals 64. Lets try these values in both equations to see if they work.

64+47=111

64-47=17

Both of those statements are true, so those are our two numbers.