Question 242285
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Let *[tex \Large x] represent the number of consecutive hits he needs.


Every time he gets a hit from now on, his number of hits increases by 1 and his number of at bats also increases by 1.  After *[tex \Large x] consecutive hits he will have *[tex \Large 20\ +\ x] hits and *[tex \Large 100\ +\ x] at bats.  His batting average will be:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{20\ +\ x}{100\ +\ x}]


Since he wants an average of at least .250, the expression above must be greater than or equal to .250.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{20\ +\ x}{100\ +\ x}\ \geq\ .250]


Solve the inequality.  If the lower bound of the interval is not an integer, round up -- he can't get a fractional part of a hit, and if you round down it won't be enough.


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