One of the fairfax county mathematics league problem

[jjuugg]

I feel like I can solve this problem easily.. However..
I can't -_-
I get three variables and I can get only 2 equations..T.T
How do you solve this!
This question makes me itchy!

"If Al gives Liz $10 and Carlo gives Liz $15, then Liz has as much money as Al and Carlo together. Instead, if Al gives Carlo $15 and Liz gives Carlo $8, then Carlo has as much money as Al and Liz together. How many dollars does Al have at the start?"

 

[Dragonfall]

Well, if I read this question correctly, Al has 48$.

 

[HallsofIvy]

I feel like I can solve this problem easily.. However..
I can't -_-
I get three variables and I can get only 2 equations..T.T
How do you solve this!
This question makes me itchy!

"If Al gives Liz $10 and Carlo gives Liz $15, then Liz has as much money as Al and Carlo together. Instead, if Al gives Carlo $15 and Liz gives Carlo $8, then Carlo has as much money as Al and Liz together. How many dollars does Al have at the start?"

You start by naming things: Let A be the amount of money Al has at the start, L the amount of money Liz has, and C be the amount of money Carlo has.

After Al gives Liz $10, he has A- 10 left. After Carlo gives Liz $15, he has C- 15 left. Liz has L+ 10+ 15= L+ 25. Then "Liz has as much money as Al and Carlo together: L+ 25= A-10+ C- 15. L+ 25= A+ C- 25 or L= A+ C- 50.

If Al gives Carlo $15, he has A- 15. If Liz gives Carlo $8, she has L- 8. Carlo has, of course, C+ 15+ 8= C+ 23. Then "Carlo has as much money as Al and Liz together: C+ 23= L-8+ A- 15= L+ A- 23: C= L+ A- 46.

You have the two equations: L= A+ C- 50 and C= L+ A- 46. What do you get if you add the two equations?

 

[jjuugg]

oh! I see the L cancels out!
Ah,,, I should have got this problem right.! T.T
Anyways thanks, now I can sleep without anxiety!lol ><

 

[HallsofIvy]

Is that Fairfax County, Virginia, U.S.A., by the way?