Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)

Question

boldjon · Answer

First, there is not enough information.  The problem cannot be solved as stated.

Second, let's assume the increase in savings was the same each month.
Month 1: 11
Month 2: 11+m
Month 3: 11+2m
Month 4: 11+3m
...
Month 57: 11 + 56m

Can you add those up?  There might be an Arithmetic Series in there, somewhere.

boldjon · Answer

Why would m = 1?

You must add up ALL the months.

11 + 11+m + 11+2m + 11+3m +  ... + 11 + 56m = 19779

57(11) + (m + 2m + 3m + ... + 56m) = 19779

m(1 + 2 + 3 + ... + 56) = 19779 - 57(11) = 19779 - 627 = 19152

m(56)(57)/2 = 19779 - 57(11) = 19779 - 627 = 19152

m = 19152*2/(56*57) -- I hope this comes out to be an integer!

m = 12 -- Woo hoo!!

11 + 23 + 35 + ... + 683 = 19779!!