Chapter 6.3, Problem 45PFA

To determine

To find the number of points that each person scored.

Answer to Problem 45PFA

Swati: 465 points

Matt: 289 points

Explanation of Solution

Given:

Swati won computer game that she played with matt.

Sum of their scores: 754

Difference of their scores: 176

Calculation:

Let x be the scores of Swati and y be the scores of Matt.

Sum of their scores is 754,

  $\Rightarrow x+y=\mathrm{754....................}(1)$

Difference of their scores is 176,

  $\Rightarrow x-y=\mathrm{176....................}(2)$

Add equations (1) and (2).

  $\begin{array}{l}\Rightarrow (x+y)+(x-y)=754+176\\ \Rightarrow x+x+y-y=930\\ \Rightarrow 2x=930\\ \Rightarrow x=465\end{array}$

Substitute the value of x in equation (2).

  $\begin{array}{l}\Rightarrow 465-y=176\\ \Rightarrow -y=176-465\\ \Rightarrow -y=-289\\ \Rightarrow y=289\end{array}$

Conclusion:

Therefore, Swati has scored 495 points and Matt has scored 289 points.