SOLUTION: Two games cost as much as five songs. The cost of two games and three songs is $16. If Joan purchased one song and one game, how much did she spend?
Question 1104159: Two games cost as much as five songs. The cost of two games and three songs is $16. If Joan purchased one song and one game, how much did she spend?
I suppose you are supposed to solve this using algebra....
But let's first think about solving it using logical reasoning.
"Two games cost as much as five songs"; "the cost of two games and three songs is $16."
Since the two games that were bought cost the same as five songs, the same $16 would have bought five songs plus three more songs, or eight songs.
8 songs for $16 means each song costs $2.
Then five songs would cost $10; and since that is the same cost as two games, each game costs 10/2 = $5.
So the cost of one song and one game would be $2+$5 = $7.
Now for the formal algebra...
(1) [2 games cost the same as 5 songs]
(2) [2 games and 3 songs cost $16]
(3) [substitute (1) into (2)]
(4) ; [solve (3) for the cost of each song]
(5) ; [substitute (4) in (1) and solve to find the cost of each game]
(6) [answer the question: what is the cost of one song and one game]
If you follow the steps, you will see the algebraic solution uses EXACTLY the same steps as the solution using logical reasoning....
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