Algebra Junior Challenges-I

$\text{first way,}$

$81 \times 15- 80 \times 14=1215-1120=95$

$\text{second way,}$

$\text{as the average is 80 for 14 students,so if Payton gets 80 number then the average of 15 students will be also 80}$ . $\text{if he gets 15 numbers more,than every student will get 1 number extra in average}$ $\text{and the average will increase.so Payton got 80+15=95 numbers}$

The average of a set of numbers is the value we get if we evenly distribute the total across all entries.

So assume that the first 14 students each scored 80.

If Payton also scored an 80 , the average would still be 80.

In order to increase the overall average to 81 , we need to add one more point to all of the scores, including Payton's.

This means we need to add a total of 15 more points, so Payton needs 80+15=95

(81 x 15) - (80 x 14)= 1,215 - 1,120= 95

$(81 \times 15)$ - $(80 \times 14)$ = $\boxed{95}$