Name: arnold
Who is asking: Student
Level: Middle

Question:
Nicole has 25 CDs and tapes altogether. When she tries to pair them up, she has 4 CDs left over. How many tapes does Nicole have?

Hi Arnold,

Imagine that she is trying to stack the tapes and CD's side by side.

If Nicole had 12 tapes then she would have 13 CD's and the CD pile would be 1 higher than the tapes pile.
If Nicole had 11 tapes then she would have 14 CD's and the CD pile would be 3 higher than the tapes pile.
If Nicole had 10 tapes then she would have 15 CD's and the CD pile would be 5 higher than the tapes pile.

She doesn't seem able to have 4 more CD's than tapes.

Try it algebrically. Let C be the number of CD's she has and T the number of tapes she has. What we know is

C + T = 25
C - T = 4

If you add these equation you get

2C = 29
so
C = 14 1/2

But C has to be an integer and hence what Nicole describes is impossible.

Cheers,
Penny
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