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Hector Villanueva has a 0.300 batting average (hits/times at bat). If she gets a total of 10 more hits the nest 10 times at bat his batting average will jump to 0.400. determine how many hits he had originally

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Answer :

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x - the numbers of hits
y - the number of times at bat

He has a 0.300 batting average.
[tex]\frac{x}{y}=0.3 \\ x=0.3y[/tex]

If he gets a total of 10 more hits the next 10 times at bat, his batting average will be 0.400.
[tex]\frac{x+10}{y+10}=0.4 \\ x+10=0.4(y+10) \\ x+10=0.4y+4 \\ x=0.4y+4-10 \\ x=0.4y-6[/tex]

[tex]x=x \\ 0.3y=0.4y-6 \\ 0.3y-0.4y=-6 \\ -0.1y=-6 \\ y=-6 \times (-10) \\ y=60 \\ \\ x=0.3y=0.3 \times 60=18[/tex]

He had 18 hits.

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