Question 262000
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You are off just a smidge...


If she rode 108 the first day, 111 the second day, etc, then she would have ridden over 800 miles in the 7 days she trained.  She only rode 126 miles total.


Let *[tex \Large x] represent the amount she rode the first day.  Then *[tex \Large x\,+\,3] is the amount she rode the 2nd day, *[tex \Large x\,+\,6] the 3rd day, and so on.


The equation becomes:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 3(0)\ +\ x\ +\ 3(1)\ +\ x\ +\ 3(2)\ +\ \cdots\ +\ x\ +\ 3(6)\ =\ 126]


Since:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\left(1\ +\ 2\ +\ 3\ +\ 4\ +\ 5\ +\ 6\right)\ =\ 3(21)\ =\ 63]


The equation simplifies to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7x\ +\ 63\ =\ 126]


*[tex \Large x] is what she rode the first day, and *[tex \Large x\ +\ 18] is what she did the last day.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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