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?

Question

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)

Answer 2

To find out how many pens a large pack contains, we need to use the information given.

Let's assume that the number of pens in a large pack is "L", and the number of pens in a small pack is "S".

We are given that Penelope bought 17 large packs and 5 small packs of identical pens. So we can write the equation:

17L + 5S = 234 (Equation 1)

However, since we don't know the value of either L or S, we need another equation to solve for them.

We also know that a total of 234 pens were on the floor, which means the number of pens in the large packs and the small packs must add up to 234. So we can write the second equation:

17L + 5S = 234 (Equation 2)

Now we have a system of two equations with two unknowns (L and S). We can solve this system of equations to find the values of L and S.

To solve the system, we can subtract Equation 2 from Equation 1:

17L + 5S - (17L + 5S) = 234 - 234

This simplifies to:

0 = 0

Since the equation simplifies to 0 = 0, we conclude that the values of L and S can be any real numbers.

Therefore, based on the given information, we cannot determine the exact number of pens a large pack contains.