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?

Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

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....
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
g, price of one game
c, price of one song

One song plus one game:

RELATED QUESTIONS
A disc jockey has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song (answered by stanbon,chandrumail)
5. Show all work. A disc jockey has 12 songs to play. Seven are slow songs, and five are... (answered by allig,lstoney)
show all work..................... a disc jockey has 7 songs to play. five are slow... (answered by edjones)
5. Show all work. A disc jockey has 10 songs to play. Seven are slow songs, and three are (answered by Alan3354)
Show all work. A disc jockey has 7 songs to play. Three are slow songs, and four are fast (answered by stanbon)
A SIDC JOCKY HAS 7 SONGS TO PLAY THREE ARE SLOW SONGS, AND FOUR ARE FAST SONGS WACH SONG... (answered by stanbon)
Show all work. A disc jockey has 11 songs to play. Eight are slow songs, and three are... (answered by stanbon)
A disc jockey has 11 songs to play. Eight are slow songs, and three are fast songs.... (answered by stanbon)
A disc jockey has 10 songs to play. Four are slow songs, and six are fast songs. Each... (answered by sudhanshu_kmr)