Piano lessons - how many minutes spent practicing

[falcios]

Deborah, Dave and Judy are practicing their piano lessons. Deb practices as long as Dave and Judy practices twice as long as Dave. If their combined practice time is 110 minutes, how long does each practice.

Answer provided in the book:
Dave 30 minutes, Deb 20 minutes, Judy 60 minutes

My question is
If Deb practices as long as Dave wouldn't their minutes be the same?
I put an x for Dave and 2x for Judy but don't know what to put for Deborah?

Can you help with this?
Thanks in advance.

 

[mmm4444bot]

Deborah, Dave and Judy are practicing their piano lessons. Deb practices as long as Dave and Judy practices twice as long as Dave. If their combined practice time is 110 minutes, how long does each practice[?]

Answer provided in the book:
Dave 30 minutes, Deb 20 minutes, Judy 60 minutes

My question is
If Deb practices as long as Dave wouldn't their minutes be the same?

No, their minutes would be the same. Therefore, the book's answer indicates a contradiction (i.e., either the answer is wrong or the exercise statement is wrong).

I put an x for Dave and 2x for Judy but don't know what to put for Deborah?

If we ignore their answer, then we would let symbol x represent Deborah's minutes also. In this case, our equation is:

x + x + 2x = 110


However, if we change the exercise statement to match the given answer, then we have:

Deborah, Dave and Judy are practicing their piano lessons. Deborah practices 2/3rds as long as Dave and Judy practices twice as long as Dave. If their combined practice time is 110 minutes, how long does each practice?

When I was a student faced with a situation like this, I would turn in both versions and invite my instructor to take their pick. :cool: