Tom F. answered • 09/29/14

Math Tutor - I can help you achieve success in math

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 = 3n

^{2 }+ 3n2(30) = 3n

^{2}+ 3n60 =3n2 + 3n

20 = n

^{2}+ nn

^{2}+ 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

Damazo T.

Thanks, again, I changed my answer.

D. Y. Taylor

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09/29/14

Damazo T.

09/29/14