Answer :
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:
[tex]=600+35=635[/tex]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:
[tex]=200+20=220[/tex]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:
[tex]=800+50=850[/tex]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:
[tex]\begin{gathered} \frac{p_3-p_2}{p_1-p_2}=\frac{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}[/tex]Thus, we will use the following parameters to solve:
[tex]\begin{gathered} p_1=635 \\ p_2=220 \\ p_3=850 \\ n_1=36 \\ n_2=17 \\ n_3=x \end{gathered}[/tex]Therefore, we can substitute and solve as shown below:
[tex]\begin{gathered} \frac{850-220}{635-220}=\frac{x-17}{36-17} \\ \frac{630}{415}=\frac{x-17}{19} \\ x-17=\frac{630\times19}{415} \\ x-17=28.84 \\ x=28.84+17 \\ x=45.84 \end{gathered}[/tex]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.
