Question

Patrick plays his guitar in a park and earns $3 for each song he plays. Hall plays his guitar at a local coffee shop and earns $9 for each song he plays, but he also has to pay a $110 fee to play at the coffee shop. Determine which equation could be used the find n, the number of songs they will have to play in order to earn the same amount of money.

Answer 1

3n = 9n - 110

Explanation:

Let's suppose that Patrick and Hall play n number of songs to earn the same amount of money.

For Patrick, the amount of money he earns is given by:

Money earned by Patrick = 3n

For Hall, the amount of money he earns after paying the $110 fee is given by:

Money earned by Hall = 9n - 110

To find the number of songs they will have to play in order to earn the same amount of money, we need to set these two expressions equal to each other and solve for n:

3n = 9n - 110

Simplifying this equation, we get:

6n = 110

Dividing both sides by 6, we get:

n = 110/6

n = 18.33 (rounded to two decimal places)

Since n represents the number of songs, it cannot be a fractional value. Therefore, we can conclude that they will have to play 18 songs to earn the same amount of money.

Therefore, the equation that could be used to find n, the number of songs they will have to play in order to earn the same amount of money, is:

3n = 9n - 110

Hope this helps!