How many ballpens are there

5 ballpens are left when 6 boxes are used and 17 ballpens are left when 5 boxes are used. How many ballpens are there?

5+6x=17+5x where x is no. Of ballpens per box
6x-5x=17-5
x=12.
THus, there are 5+6(12)=77 ballpens

Suppose you have n ballpens, and in a box are k of them.

5 ballpens are left when 6 boxes are used ⇒ n = 6k + 5

17 ballpens are left when 5 boxes are used ⇒ n = 5k + 17

⇒ 6k + 5 = 5k + 17
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k = 12 ballpens in a box
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⇒ there are 6*12 + 5 = 77 ballpens

17+5=22 ballpoint pens