Question

Hi, I am having trouble with this. Could you help? This month a band plays 3 private parties, each of which pays them the same amount. However, the band also has $200 in travel expenses. Taking those expenses into account, they make a total of $2500. The following month, the band has 5 bar gigs and 2 private parties, plus they make an additional $800 (total) by selling merch, and have a total of $350 in travel expenses. With all expenses factored in, they make a total of $4125. How much, on average, is the band payed per bar gig? (assume they are paid the same amount per party this month as they were last month). Write 2 algebra equations then solve.

Answer 1

We have two cases. The first month, they played in 3 private parties that payed the same. They had a cost of $200 in travel and, in the end, they made $2500. Let "p" be the paid amount of each party. Since there were 3, they were payed 3*p. If we then substract their expenses of $200, we get the final amount, that should be equal to $2500.

In an equation, this is:

`\begin{gathered} 3p-200=2500 \\ 3p=2500+200 \\ 3p=2700 \\ p=(2700)/(3) \\ p=900 \end{gathered}`

So, each party payed $900.

In the second month, they worked on 5 bar gigs and 2 private parties. We already know that each private party pays $900, so, if "b" is the average amount they made in each bar gig, then "5b" will be the total they made in bar gigs and, adding the party amount, we have, in the second month:

`5b+2p=5b+2\cdot900=5b+1800`

The had $350 travel expenses, so we need to substract this and we should end up with the total they made, that was $4125:

`\begin{gathered} 5b+1800-350=4125 \\ 5b+1450=4125 \\ 5b=4125-1450 \\ 5b=2675 \\ b=(2675)/(5) \\ b=535 \end{gathered}`

Thus, on average, they were payed $535 per bar gig.