Question 628326: please , i find it difficult deducing the equation in this problem
Timmy enjoys playing old-fashioned video games. He found 3 game systems on eBay and wants to purchase a Nintendo game system, an Atari game system, and a Sega arcade game system. The Sega system costs $600 more than the sum of the Atari and the Nintendo systems. All together, the three game systems cost $11,000. The Atari system costs $1100 less than the Nintendo. Determine how much Timmy paid for each game system.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! First, assign letters to the unknown quantities you are looking for:
Let:
A = the cost of the Atari system.
N = the cost of the Nintendo system.
S = the cost of the Sega system.
Next, write down the problem in algebraic notation using the variable (unknown) letters.
1) A+N+S = $11,000 "All together, the three game systems cost $11,000"
2) S = (A+N)+$600 "The Sega system costs $600 more than the sum of the Atari and the Nintendo systems."
3) A = N-$1100 "The Atari system costs $1100 less than the Nintendo."
Now you have a system of three equations with three unknowns (A, N, and S).
You can use a number of methods to solve this sytem of equations, one of which is "substitution".
Start with:
A+N+S = $11,000 now substitute the S from equation 2) to get:
A+N+((A+N)+$600 = $11,000 Simply this.
2A+2n+$600 = $11,000 Subtract $600 from both sides.
2A+2N = $10,400 Now divide both sides by 2 to further simplify.
A+N = $5200 Substitute the A from equation 3) to get:
(N-$1100)+N = $5200 Simplify.
2N-$1100 = $5200 Add $1100 to both sides.
2N = $6300 Divide both sides by 2.
N = $3150 The Nintendo system costs $3150.
From here you should be able to work out the rest of the problem.
If you still have trouble, re-post.
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