What is the most the pen could count

Question

Jim and Barbara each want to buy the same kind of pen. Jim still needs 24 cents to buy the pen and Barbara still needs 4 cents to buy the pen. If they combine their money, they still do not have enough. What is the most the pen could cost?

Answer 1

You can solve this algebraically:

if the pen costs p, Jim has p - 24 and Barbara has p - 4.

If together they have less than p,

p - 24 + p - 4 < p

2p - 28 < p

p < 28

The most the pen can cost is 27 cents.

Alternatively, Barbara needs 4 more cents, so if getting Jim's money is not enough, p- 24 < 4; p < 28

Answer 2

p is the cost of the pen

Jim has p - 24, Barbara has p - 4.

Together they have 2p - 28.

Yet that is less than than p, 2p - 28 < p.

p < 28

The most the pen could cost is 28 cents