Penelope bought 17 large packs and 5 small packs of identical pens. When she got home, her little sister opened all of the packages on the floor. If a total of 234 pens were on the floor, how man pens did a large pack contain?

Answer 1

Here we have
L=Size of large packs, L∈ℕ
S=Size of small packs, S∈ℕ
with the conditions
1. L>S
2. 17L+5S=234

The integer solutions to L are:
L=2 =>S=(234-2*17)/5=40
L=7 =>S=(234-7*17)/5=23
L=12 =>S=(234-12*17)/5=6

So make your choice according to the constraints from the following:
(2,40),(7,23),(12,6)