Question

word problemA band goes on tour to play similar size clubs in cities where it seldom tours. At one city the band has 35 people on its mailing list, and promoters pass out 600 flyers. The club reports that 36 more people are there than when an unknown band which does no promotion plays. At the second city the band has 20 people on its mailing list and promoters pass out 200 flyers. The club reports that 17 more people are there than when an unknown band does no promotion plays. The band plans to play a city where there are 50 people on the mailing list and pass out 800 flyers. How many more people does the band expect to bring to the show than an unknown, un-promoted band would bring?

Answer 1

The following information is given about the different cities:

City 1:

Number of fliers: 600

Number on the mailing list: 35

Total number of people the promotion reached:

`=600+35=635`

Number of more people present: 36

Therefore, a promotion reaching 635 people will have 36 more people.

City 2:

Number of fliers: 200

Number on the mailing list: 20

Total number of people the promotion reached:

`=200+20=220`

Number of more people present: 17

Therefore, a promotion reaching 220 people will have 17 more people.

City 3:

Number of fliers: 800

Number on the mailing list: 50

Total number of people the promotion reached:

`=800+50=850`

Number of more people present: x

We can find the value of more people in City 3 by interpolation. The interpolation formula is given to be:

`\begin{gathered} (p_3-p_2)/(p_1-p_2)=(n_3-n_2)/(n_1-n_2) \\ \text{where} \\ p=\text{ Number of people the promotion reached} \\ n=\text{ Number of more people present} \end{gathered}`

Thus, we will use the following parameters to solve:

`\begin{gathered} p_1=635 \\ p_2=220 \\ p_3=850 \\ n_1=36 \\ n_2=17 \\ n_3=x \end{gathered}`

Therefore, we can substitute and solve as shown below:

`\begin{gathered} (850-220)/(635-220)=(x-17)/(36-17) \\ (630)/(415)=(x-17)/(19) \\ x-17=(630*19)/(415) \\ x-17=28.84 \\ x=28.84+17 \\ x=45.84 \end{gathered}`

Since the number cannot be a decimal, the number will be approximately 46.

ANSWER:

The number of people the band expects more than an unpromoted band will be 46 people.