The numbers of blue, red, green and black pencils are proportional to the numbers 2, 3, 5, and 7, respectively. if we add the number of the difference of black and green pencils, and the number of the difference of red and blue pencils, then we will get 12. how many green pencils are there?

  20 green pencils

Step-by-step explanation:

The difference between black and green "ratio units" is 7 -5 = 2. The difference between red and blue ratio units is 3 -2 = 1. The sum of those differences is 2 +1 = 3 ratio units, which represent 12 pencils. Then each ratio unit represents 12/3 = 4 pencils.

The 5 ratio units of green pencils represent 5·4 pencils = 20 green pencils.

If you need an equation, you can use k as the constant of proportionality. Then the sum of differences described is ...

  (7k -5k) + (3k -2k) = 12

  3k = 12 . . . . simplify

  k = 4 . . . . . . divide by 3

  5k = 5·4 = 20 . . . . . number of green pencils