THIS WAS DUE YESTERDAY, with a lot of other confusing problems! Please help! (all algebraic)

Question

Mr. Myers wants to join a music club. The 1st choice music club charges a $5 sign-up fee and $1 each song.The superstar music club charges no sign-up fee and charges $3.50 each song. After how many song will the cost of the music clubs be equal? 1st choice music club equation: _____

Superstar Music Club Equation: _____

Solution: _(_,_)_

Answer 1

We need a bit of algebra with C = Cost and S = Songs

In general, C = sign-up + persong.S which is the slope intercept form of a straight line with Cost as the y axis, and Songs as the x axis. Sign up is the y intercept. And persong charge is the gradient of the line. So, if you want, we can easily plot the equations on Desmos Graphing or similar. You can then solve graphically by finding the point of intersection on the graph.

1st Choice equation is C = 5 + 1S (or C = 5 + S)

And Superstar equation is C = 0 + 3.5S (or C = 3.5S)

Solution is when they have same cost, so 5 + 1S = 3.5S

=> 2.5S = 5

=> S = 2

Hence they are equal at 2 songs.

Double-check by putting these numbers in the equations: 5 + 1(2) = 7 and 3.5(2) = 7 also. Hence the interesection point is (2, 7).