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System of Equations: Raising Funds

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Two teams need to raise $1,000 each for their end-of-the-year field trips. Team A wants to sell hot dogs at the games, and Team B wants to sell nachos. It costs $20 to rent a hot dog roller and it costs $10 to rent a nacho chip warmer. The cost of additional supplies for the hotdog is $0.02 per tray. The additional cost for the nachos is $0.06 per container. Team A will sell the hot dogs for $1.50 each. Team B will sell the nachos for $1.00 each.

1) Create a system of equations to model the profit for each time.
2) Graph the system of equations for problem #1.
3) How many hot dogs will Team A need to sell to reach their goal?
4) How many nachos will Team B need to sell to reach their goal?
5) What is the least number of items Team will need to sell to avoid losing money?
6) What is the least number of items Team B will need to sell to avoid losing money?
7) At what point do both teams earn the same amount of profit? How do you know and how much profit is earned?

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The solution provides step-by-step solving of the given problem providing a system of equations.

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1)
Let the number of hot dogs that Team A sells be x1 and the number of nachos that Team B sells be x2.
It costs $20 to rent a hot dog roller, which is the fixed cost. The cost of additional supplies for the hotdog is $0.02 per tray, which is the variable cost. The selling price of hot dogs is $1.50 each.
The equation to model the profit for Team A, according to the given conditions, is as follows:
Profit,P_A=(1.50-0.02) ...

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