One of the fairfax county mathematics league problem

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Discussion Overview

The discussion revolves around a mathematics problem from the Fairfax County Mathematics League, focusing on a scenario involving three individuals and their monetary exchanges. Participants explore how to set up equations based on the problem's conditions to determine how much money Al has initially.

Discussion Character

  • Homework-related, Mathematical reasoning, Exploratory

Main Points Raised

  • One participant expresses frustration about having three variables but only two equations, indicating difficulty in solving the problem.
  • Another participant proposes that Al has $48, suggesting a potential solution without detailed justification.
  • A later reply outlines a method for setting up equations based on the problem's conditions, defining variables for Al, Liz, and Carlo's initial amounts and deriving two equations from the given scenarios.
  • One participant realizes that by adding the two derived equations, the variable for Liz cancels out, indicating a simplification in the problem-solving process.
  • Another participant expresses relief after understanding the solution process, indicating that they feel more at ease with the problem.
  • A question is raised about the geographical context of the Fairfax County Mathematics League, specifically whether it refers to Fairfax County, Virginia, U.S.A.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution, as one proposes a specific answer while others engage in the problem-solving process without confirming the correctness of that answer.

Contextual Notes

The discussion includes assumptions about the variables and the relationships between them, which may not be fully explored or resolved. There are also unresolved mathematical steps in deriving the final answer.

jjuugg
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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?"
 
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Well, if I read this question correctly, Al has 48$.
 
jjuugg said:
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?
 
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 ><
 
Is that Fairfax County, Virginia, U.S.A., by the way?
 

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