Question

a website allows users to download individual songs or an entire album. All individual songs cost the same to download and all albums cost the same to download. Ryan pays $14.94 to download 5 individual songs on 1 album. Seth pays $22.95 to download 3 songs and 2 albums. How much does the website charge to download a song? An entire album?

Answer 1

Start by finding how much individual songs cost... Ryan downloaded 5 songs and paid $14.94. So you could divide to find out how much each song costs.

Once you know that, you can multiply the price per song by the 3 songs that Seth downloaded... that will tell you how much of his $22.95 expense was from the 3 individual songs.

Then, you can subtract the 3-song cost from $22.95 to get the price for 2 albums, and you can then divide that price by 2 to get the price for 1 album.

It's several steps, but each step is easy.

Answer 2

how would you do this for solve systems of elimination?

Answer 3

I suppose you could set up the system using variables like "s" for price of a song and "a" for price of an album.

Ryan: 14.94 = 5s
Seth: 22.95 = 3s + 2a

So you could multiply Ryan's equation by 3 and Seth's equation by -5 and then add them together to eliminate the "s" terms and then solve for "a". Then you end by solving Seth's equation using the "a" price you found and solving for "s".

Answer 4

that doesnt help me..

Answer 5

Ryan: 14.94 = 5s
Seth: 22.95 = 3s + 2a
Now multiply the "Ryan" line by 3: Ryan: 3(14.94) = (3)(5s)
and the Seth line by -5: Seth: (-5)(22.95) = (-5)(3s) + (-5)(2a)
+ _____________________________________
Then add the two new lines: 3(14.94) - 5(22.95) = -10a
to eliminate "s"
Then simplify that expression and solve for "a", the price of one album

Answer 6

so one of the answers would be -15.95??

Answer 7

It shouldn't be negative... it's a price.

3(14.94) - 5(22.95) = -10a
44.82 - 114.75 = -10a
-69.93 = -10a

a = -69.93/(-10) = 6.993 then round to 6.99. So albums cost $6.99

Answer 8

oops sorry i forgot two negatives equal a positive.

Answer 9

how much does the website charge for each song downloaded? how do i find that?

Answer 10

No worries... so if you have a = 6.993, can you put that back into the Seth equation to find out how much each song costs?

Seth: 22.95 = 3s + 2a
and you know a = 6.993...
22.95 = 3s + 2(6.993)

Answer 11

so about $2.99 per song? cause its 2.988 round up?

Answer 12

That looks correct.

You can double check it too... remember Ryan spent $14.94 to buy 5 songs...

So 14.94 should be equal to 5 * 2.988.

Good work :)

Answer 13

Thank you! Help with the another one?

Answer 14

Can you post it as a new question?

Answer 15

Yep! Tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets. Find the number of tickets sold to students and the number of tickets sold to adults. And again its the elimination method.

Answer 16

Try to set up the system... then I will help you work through it.

Answer 17

3x+5y=2995
x+y=729

Answer 18

Great... which variable do you want to eliminate first? It's up to you... either x or y is fine. in this case.

Answer 19

x

Answer 20

Ok, so you want to multiply that 2nd equation by some number to make it so that when you add it to the first equation, the "x" terms are eliminated.

There is a "3x" in the first equation, so you would want to multiply the 2nd equation by "-3" to create a -3x term in that 2nd equation.

3x+5y=2995
x+y=729

3x + 5y = 2995
-3(x+y) = -3 * 729
-3x - 3y = -2187

Answer 21

So Equation 1 is: 3x + 5y = 2995
and the new Eq 2 is: -3x - 3y = -2187
---------------------------------------
add them together: 3x - 3x + 5y - 3y = 2995 - 2187
to eliminate "x"

Answer 22

Okay i think i got it. 325 adults and 404 students.

Answer 23

Looks good... do you get the idea of the elimination method now?

Answer 24

yes i do. Thank you!

Answer 25

Great... glad to help :)