Question 702397
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Let *[tex \LARGE S] be the Sarah function and *[tex \LARGE F] be the Felicia function. Then let *[tex \LARGE x] represent the number of weeks after the beginning of summer.


The *[tex \LARGE S(x)] is the amount of money Sarah has after *[tex \LARGE x] weeks.  Since she starts with $250 and <i>increases</i> $150 each week, we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ S(x)\ =\ 250\ +\ 150x]


Likewise, for Felicia (but this time reducing the amount each week):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ F(x)\ =\ 1650\ -\ 200x]


Draw your grid so that you have 1 week increments horizontally and either $50 or $100 increments vertically (otherwise you'll need a scroll as long as Santa's naughty list to get it all on one piece of paper).


Pick a small value for *[tex \LARGE x], substitute into the Sarah function.  Do the arithmetic to calculate the value of the function, then create an ordered pair, *[tex \LARGE (x,S(x))].  Plot the point.  Repeat with a new value of *[tex \LARGE x].  Draw a line through your two points.


Repeat the whole process with *[tex \LARGE F(x)].


If the two lines intersect, then the ordered pair that describes the intersection point gives you the week number after which the bank accounts will be equal and the value of each of the accounts at that time.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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