Chapter 1.1, Problem 57E

(a)

To determine

To find the number of hits player $A$ have in the year $2011$ -

  

Answer to Problem 57E

The number of hits in $2011$ by player $A$ is $132$ .

Explanation of Solution

Given:

  

Batting Average in $2011$$=.296$

At-bats in $2011$$=446$

Formula Used:

Batting Average $=$ Number of hits $÷$ Number of At-bats

Calculation:

Given:

Batting Average in $2011$$=.296$

At-bats in $2011$$=446$

Let the number of hits be $N$ .

As per the given formula, we have:

Batting Average $=$ Number of hits $÷$ Number of At-bats

  $0.296=N÷446$

Solving the above equation, we have:

  $\begin{array}{l}0.296=N÷446\\ N=0.296\times 446\\ N=132.016\end{array}$

Rounding off to the nearest whole number $N=132$ .

Thus, the number of hits in $2011$ by player $A$ is $132$ .

Conclusion:

Hence, the number of hits in $2011$ by player $A$ is $132$ .

(b)

To determine

To determine if the friend is correct or not.

  

Answer to Problem 57E

The friend is wrong as Number of At-bats will be less for player $B$ .

Explanation of Solution

Given: Forplayer $A$

  

Formula Used:

Batting Average $=$ Number of hits $÷$ Number of At-bats

Calculation:

Given:

Number of hits in $2011$ by player $A$ is $132$ .

Number of hits in $2011$ by player $B$$=$$132-33$ .

Number of hits in $2011$ by player $B$$=$$99$ .

Batting Average of player $B$ is greater than player $A$ .

Thus, using the above formula, we have

Number of At-bats $=$ Number of hits $÷$ Batting Average

Since, Batting Average of player $B$ is greater and Number of hits is also less.

Thus, Number of At-bats will be less for player $B$ .

Conclusion:

Hence, the friend is wrong as Number of At-bats will be less for player $B$ .