how to set up a proportion with this info

Question

There were 30 campers in Crazy Creek Park on Saturday when it started to rain. In the first hour of rain, 3 campers took down their tents and went away. In the second hour, 6 campers took down their tents and left the park. The rain kept pouring down. Every hour 3 more campers left than during the hour before. In what hour did the last campers leave the park?

Answer 1

You can solve this using an arithemtic series

 

The 1st hour 3 left

The 2nd hour 6 left

The 3rd hour 9 left

 

So the numbers in your arithmetic series are 3, 6, 9, 12, ....

 

You want to find the sum of the series when it is equal to 30, the total number of campers

 

Actually that would be in the 4th hour since 3+6+9+12=30 but you can solve it mathematically as follows

 

S =n/2(1st term + last term)

 

We know the first term is 3

We don't know the last term but we can write it as (3 + (n-1) 3)

 

S = n/2 (3 + (3 + (n-1)3)

 

S = n/2 (3n + 3)

 

2S = 3n² + 3n

 

2(30) = 3n² + 3n

 

60 =3n2 + 3n

 

20 = n² + n

 

n² + n -20 = 0

 

(n+5)(n-4)=0

 

n+5 = 0   n=-5 won't work we need a postive number

 

n -4 =0     n=4       The campers will be gone in four hours

Answer 2

Hello,  Mimi

 

Sorry, that I gave you the wrong answer.  I misread the problem.  This should be it.

By the end of the ninth hour everybody has left:

Ok, you started with 30 campers

End of 1st =30-3=27

End of 2nd= 27-6= 21

End of 3rd= 21-9= 12

End of 4th= 12-12=0

 

There you go.  Keep posting questions.

 

D.Y. T.