Chapter 6.4, Problem 28PPS

To determine

To calculate the correct score of the student.

Answer to Problem 28PPS

95

Explanation of Solution

Given:

Mrs. Henderson accidentally reversed the digits of a test score and did not give a student 36 points.

Sum of the digits 14 and agreed to give the student his correct score plus extra credit.

Calculation:

Let x be the tens digit of the student’s score and y be the ones digit of the score.

Then the correct score of the student is $10x+y$ .

The incorrect score of the student is $10y+x$ , since the digits are reversed.

It is given that the teacher did not give the student 36 points.

That is the difference of the correct score and the incorrect score is 36 points.

  $\begin{array}{l}\Rightarrow (10x+y)-(10y+x)=36\\ \Rightarrow 9x-9y=36\\ \Rightarrow x-y=\mathrm{4.............................}(1)\end{array}$

Given that the sum of the digits is 14.

  $\Rightarrow x+y=\mathrm{14.............................}(2)$

Add equation (1) and equation (2),

  $\begin{array}{l}\Rightarrow (x-y)+(x+y)=14+4\\ \Rightarrow 2x=18\\ \Rightarrow x=9\end{array}$

Substitute the value of x in equation (1),

  $\begin{array}{l}\Rightarrow 9-y=4\\ \Rightarrow -y=4-9\\ \Rightarrow y=5\end{array}$

Conclusion:

Therefore, the score of the student is 95.