Hard Thinking/ Math Problem... my mom gave me this problem to solve... please help. :]?

Question

A person buys 20 pencils for 20 cents.

There are 3 different types of pencils.

Pencil A costs 4 cents.

2 pencils of Pencil B cost 1 cent.

4 pencils of Pencil C cost 1 cent.

You have to have at least one purchase of each pencil. What combination of purchases will work?

Answer 1

3 x A = 12

6 x B = 3

20 x C = 5

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total = 20

Answer 2

It can be done. I'm not gonna tell you how though, since this is the NPR weekend edition puzzler this week.

Here's a hint: don't think about it in terms of money.

Answer 3

i might be wrong. but i have been working on this and its not possible.

say the first fraction is the ammount of money and the last fraction is the ammount of pencils....you want the answer to be 20/20.

A: 4/1

B: 1/2

C: 1/4

if you get 4 of each A and C you get 20/20 but it isnt possible when you have to include B.

closest i could get is 19/19. Which is A:1 B:6 C:3