SOLUTION: Your grandmother offers to give you, for the whole year, • Deal A: 5 cents each day, or • Deal B: 0 cents on day 0, 1 cent on day 1, 2 cents on day 2, 3 cents on day 3, and so f

Algebra ->  Linear-equations -> SOLUTION: Your grandmother offers to give you, for the whole year, • Deal A: 5 cents each day, or • Deal B: 0 cents on day 0, 1 cent on day 1, 2 cents on day 2, 3 cents on day 3, and so f      Log On


   



Question 951566: Your grandmother offers to give you, for the whole year,
• Deal A: 5 cents each day, or
• Deal B: 0 cents on day 0, 1 cent on day 1, 2 cents on day 2, 3 cents on
day 3, and so forth.
Which deal would you accept, Deal A or Deal B? Show that the deal you chose
is better than the other deal.
I know the equation for Deal A is f(x)= .05x
but having a hard time with the non-linear Deal B...Thoughts?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll say there are +365+ days / year
Deal A: +.05%2A365+=+18.25+ dollars / year
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Deal B:
You have:
+.01+%2B+.02+%2B+.03+%2B+.04+ . . . etc.
There's a formula for this sequence:
+%28+n%2A%28+n%2B1+%29%29+%2F+2+ gives you 1 + 2 + 3 + 4 + . . . n
So, I'll say +n+=+365+ and multiply the result by +.01+
+%28+365%2A366+%29+%2F+2+=+133590%2F2+
+133590%2F2+=+66795+
+.01%2A66795+=+667.95+
------------------------
Deal B is better by +667.95+-+18.25+=+649.70+
Hope I got it