Question #95279

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Answer 1 · 2017-10-22T04:42:51

$640$ $640$ at bats

To find batting average, you have to divide the number of hits by the number of at bats.

The first part of the season he has an average of $\frac{64}{256}$ $64/256$

So he had 64 hits in 256 at bats in the first part of the season.

The second part of the season he has an average of $.300$ $.300$

Let $x =$ $x=$ number of hits in the second part of the season
And $y =$ $y=$ number of at bats in the second part of the season

Thus $\frac{x}{y} = .300 \to x = .300 y$ $x/y=.300->x=.300y$

For the entire season he has an average of $.280$ $.280$

Since his total season average was $.280$ $.280$ ,

$\frac{64 + x}{256 + y} = .280$ $(64+x)/(256+y)=.280$

Plug in the first equation for $x$ $x$ :

$\frac{64 + .300 y}{256 + y} = .280$ $(64+.300y)/(256+y)=.280$

Solve for $y$ $y$ :

$64 + .300 y = .280 (256 + y)$ $64+.300y=.280(256+y)$

$64 + .300 y = 71.68 + .280 y$ $64+.300y=71.68+.280y$

$.020 y = 7.68$ $.020y=7.68$

$y = 384$ $y=384$ , so he had a total of $384$ $384$ at bats in the 2nd part of the season

Therefore he had a total of $256 + 384 = 640$ $256+384=640$ at bats