Two Simple Equations

You have apples and peaches. All together there are 12 fruits. There are two more apples than peaches. How many of each fruit are there? Note that similar problems do not always have a solution. Try to think of when they do and when they do not.

Please try switching to IE 11 (Windows) or Safari (Mac), for no other browser nowadays runs Java applets. If asked whether to allow the applet to load, click Yes - the applet is signed with a security certificate from a trusted company. But, regardless, there is an explanation below.

What if applet does not run?

(You may notice that the problem of the total of, say, 12 fruits, in which there are 3 more apples than peaches has no solution. One reason is that due to the counting nature of the problem we are looking for an integer solutions. But there could not be two whole numbers whose sum is even, while the difference is odd. For additional brooding, see the page on Math reform and thoughts of where mathematics starts.)

71948705