Expert: Josh - 5/13/2006

Question
Please help me solve this problem
Sept. $4,200 Oct. 18% more than Sept.
Nov. and Dec. 10% more than both the previous two months?

i worked it out like this
4,200X.18=$4,956 Sept 4,200+Oct 4,956=9,156X.10=$10,071.60+4,200= $14,271.60 this is my answer, could you please let me know if I solved it correctly?
Thank you very much.

Answer
Hi Cam,

The string of numbers is quite hard to read, it looks rather like the mathematical equivalent of a runaway sentence. It would be nice if you could add some space to break things up a little.

Let x(9)=4200, x(10), x(11) and x(12) be the amount of money for the month of September, October, November and December, respectively.

October sees an increase of 18% to the previous month, so
x(10)=1.18*x(9)=1.18*4200=4956 ...[#1]
I am confident that you've got this right.

However, the meaning of the next part is unclear. Not really sure how you would interpret "Nov. and Dec. 10% more than both the previous two months"?

1st possibility:
Do you mean that "the amount for November (respectively, December) is 10% more than the previous month?
 In this case, x(11)=1.1*x(10) and x(12)=1.1*x(11), where the value for x(10) is given in [#1] above.

2nd possibility:
Do you mean that "the amount for November (respectively, December) is 10% more than the combined total in the previous two months [viz., Nov=1.10*(Sept+Oct); Dec=1.10*(Oct+Nov)]"
 In this case, x(11)=1.1*[x(10)+x(9)] and x(12)=1.1*(x(11)+x(10))

3rd possibility:
Do you mean that "the amount for November, and similarly, the amount for December are both given by a 10% increase on the combined total of September and October?
 If this is the case, then, x(11) = x(12) = 1.1*[x(10)+x(9)].

I'm not sure if you need to find the amount of money accumulated from September to December, but that's easy enough to do, once we sort out the meaning of the question (which of the alteratives above is applicable).

The accumulated amount is x(9)+x(10)+x(11)+x(12) OR x(9)+x(10)+x(11). The latter assumes the amount for Nov and Dec are consolidated into x(11).

Hope the systematic approach helps you solve the problem.
It's generally easier to break things up into smaller parts.