SOLUTION: the sum of two numbers is 92. their difference is 20. find the numbers

Click here to see ALL problems on Linear Equations And Systems Word Problems

Question 1209578: the sum of two numbers is 92. their difference is 20. find the numbers
Found 3 solutions by ikleyn, timofer, greenestamps:
Answer by ikleyn(52799)   (Show Source):
You can put this solution on YOUR website!
.

Mentally in your mind, make your greater number 20 units less.

You will have two equal numbers with the sum of 92 - 20 = 72.

Hence, the smaller of the two original numbers is 72/2 = 36.

Then the greater of the two original numbers is 36 + 20 = 56.

ANSWER.   The numbers are 36 and 56.

To complete the solution in full, check mentally that the difference of the found numbers is 20 and the sum is 92.

Solved mentally.

--------------------

I wrote this post to show you that this simple problem
can be solved mentally without using equations.

As well as a million of other similar simple problems.

Answer by timofer(105)   (Show Source):
You can put this solution on YOUR website!

same as

36 and 56

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Here is another informal solution method that can be done mentally.

Consider the numbers on a number line.

You start at the first number and move one direction a distance equal to the second number and end up at 92; or you move the other direction the same distance and end up at 20.

That means the first number is halfway between 92 and 20 -- i.e., it is the average of 92 and 20. So the first number is (92+20)/2 = 56.

Then the second number is the number you need to add to 56 to reach 92: 92-56 = 36.

ANSWERS: 56 and 36