Chapter 6.4, Problem 36PFA

To determine

To find the number of points that a player earns for a double play

Answer to Problem 36PFA

17 points

Explanation of Solution

Given:

The table represents the number of each kind of play made by each player and each player’s score at the end of the game.

Calculation:

Let x be the number of points for single play and y be the number of points for double play.

The score of Nick can be formulated as:

  $16x+5y=\mathrm{197........................}(1)$

The score of Cal can be formulated as:

  $9x+6y=\mathrm{165.........................}(2)$

Multiply equation (1) with 6 and equation (2) with 5

  $96x+30y=\mathrm{1182........................}(3)$

  $45x+30y=\mathrm{825..........................}(4)$

Subtract equation (4) from equation (3). Then,

  $\begin{array}{l}\Rightarrow (96x+30y)-(45x+30y)=1182-825\\ \Rightarrow 51x=357\\ \Rightarrow x=7\end{array}$

Substitute the value of x in equation (2),

  $\begin{array}{l}\Rightarrow 9(7)+6y=165\\ \Rightarrow 63+6y=165\\ \Rightarrow 6y=102\\ \Rightarrow y=17\end{array}$

Conclusion:

Therefore, a player earns 17 points for double play.