If the circulation for newspaper 1 is 386 thousand more than the circulation for newspaper? 2, and their combined circulation is 2510 ? thousand, find the circulation for each newspaper.

Step-by-step explanation:

Let "a" and "b" represent the circulations of papers 1 and 2 in thousands, respectively. From the problem statement, we have ...

  a -b = 386

  a +b = 2510

Adding these two equations gives ...

  2a = 2896

  a = 1448 . . . . . . divide by 2

  b = 1448 -386 = 1062

The circulation numbers are 1448 thousand and 1062 thousand for papers 1 and 2, respectively.

Comment on the problem and solution

This is what I call a "sum and difference" problem. You can see that we found the larger of the two numbers (paper 1 circulation) by adding the given numbers and dividing that result by 2.

This generic procedure can be used to solve any "sum and difference" problem: add the given numbers and divide by 2. This will give the larger of the two numbers being sought. The smaller one can be found by subtracting that from the sum, or by subtracting the difference. (In this problem, we subtracted the difference.)

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap