SOLUTION: At the arcade, Ryan Sara and Tom played video racing games, pinball and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Tim spent $12.25 fo

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Question 675206: At the arcade, Ryan Sara and Tom played video racing games, pinball and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games and 4 games of air hockey. How much did each of the games cost?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 3 unknowns in this problem, but only
2 equations. That usually means some extra figuring
or guesswork.
Let +r+ = the cost of a racing game
Let +p+ = the cost of a pinball game
Let +a+ = the cost of air hockey
-----------------------------
(1) +6r+%2B+2p+%2B+a+=+6+
(2) +2r+%2B+7p+%2B+4a+=+12.25+
--------------------------
Note from (1), that
+r+%3C=+1+
+p+%3C=+3+
+a+%3C=+6+
----------
and, from (2)
+r+%3C=+6.12+
+p+%3C=+1.75+
+a+%3C=+3.06+
-------------
From these 2, I get
+r+%3C=+1+
+p+%3C=+1.75+
+a+%3C=+3.06+
--------------
I'll take some guesses
+r+=+.75+
+p+=+1+
+a+%2B+2.5+
Now to test them:
(1) +6r+%2B+2p+%2B+a+=+6+
(1) +6%2A.75+%2B+2%2A1+%2B+2.5+=+6+
+r+ looks too big. I'll say
+r+=+.35+
(1) +6%2A.35+%2B+2%2A1+%2B+2.5+=+6+
(1) +2.1+%2B+2+%2B+2.5+%3E+6+
I'll say +a+=+1.75+
(1) +6%2A.35+%2B+2%2A1+%2B+1.75+=+6+
This is the only way to solve if you
have more unknowns that equations.
If you keep playing with it, you'll
get closer to the answer.