Question 1204043: The sum of two numbers is -22. The difference of the two numbers is 8. What are the numbers? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52765) (Show Source):
x + y = -22
x - y = 8
------------------- Add these equations to get
2x = -22 + 8 = -14 ---> x = -14/2 = -7; y = -22 - x = -22 - (-7) = -22 + 7 = -15.
ANSWER. The numbers are -7 and -15.
Solved.
There are other ways to solve, but this one is the most educative (in my view).
The solution shown by tutor @ikleyn is probably the easiest, most straightforward way to solve the problem using formal algebra.
Of the many other ways to solve the problem that she mentions, there is one that I find to be a quick and easy informal method, using logical reasoning and simple mental arithmetic.
We are given that the sum of two numbers is -22 and the difference is 8.
If we picture that on a number line, then we start at the first number and go a distance equal to the second number in one direction to end up at -22, and we start at the first number and go a distance equal to the second number in the other direction to end up at 8.
That means the first number is halfway between -22 and 8.
So the first number is the average of -22 and 8; and then the second number is the difference between that average and either -22 or +8.
First number: (-22+8)/2 = -7
Second number: (-22)-(-7) = -15 (or (-7)-(8) = -15)
