Question

Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers. The game gave Chase four villagers to start with. Help Chase expand his empire by solving for how many villagers he can create with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

Answer 1

I have found that he will have 28.17 villagers in the 17th village but I am having trouble making and equation.

Answer 2

making an equation*

Answer 3

@Jonask

Answer 4

@ParthKohli

Answer 5

@Preetha

Answer 6

\[\text{let number of towns be } t\\ \text{let number of villagers be }v \]
Each town he has allows him to create 1.13 times as many villagers,implies
\[t=1.13v\]
then since he starts with 4 villagers we have
\[17=1.13(v+4)\implies v=\frac{17}{1.13}-4\]
in general
\[t=1.13(v+4)\implies v=\frac{t}{1.13}-4\]

Answer 7

Okay. So if I wanted to solve for any other village I would use the equation t=1.13(v+4), plug in for t and solve for v?

Answer 8

yes i suppose thats the way to do it ,although the number of villagers is not an integer ,but its game anyway

Answer 9

Okay thanks so much!!