Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent fewer than he sold, approximately what percent of the pears did he sell?

I do not see why you would add 2.5p in the total number of pears picked should be the sum of the pears poached and canned. Which would be p +1.4p. Please email me asap with justification of why 2.5p was added.

We have to set up a couple of equations

Let S be the number he sold
Let C be the number he canned and = (1+0.4)P
Let P be the number he poached and = (1-0.6)S

Remember when something is increasing by some percent that we can express as the decimal r, then, it is increasing by a factor of (1+ r). Similarly when decreasing, it decreases by a factor (1- r).

So we want to know what S / (S + C + P) equals:

So we have: S / [S + (1.4)(0.4)S + (0.4)S] notice we substituted everything to be in terms of S. Now, we can cancel the S term from everything and we have:

1/ (1 + 0.56 + 0.4) = 1/1.96 = 1/ (196/100) = 100/196 = 0.51 = 51%