Problem:
Zelda played the Adventures of Math game on August 1 and scored 1700 points. She continued to play daily over the next 5 days. The bar chart below shows the daily change in her score compared to the day before. (For example, Zelda's score on August 2 was 1700+80=1780 points.) What was Zelda's average score in points over the 6 days?
Daily Change in Score from August 2 to 6
Aug 2 Aug 3 Aug 4 Aug 5 Aug 6
Answer Choices:
A. 1700
B. 1702
C. 1703
D. 1713
E. 1715
Solution:
The table below shows Zelda's daily scores over the 6 days.
DateAug1Aug2Aug3Aug4Aug5Aug6​Change+80−90−10+60−40​Score170017801690168017401700​​
Summing the scores and dividing by 6 gives an average of
61700+1780+1690+1680+1740+1700​=610290​=(E)1715​ points.
OR
The bar chart below shows the cumulative change in Zelda's score relative to the 1700 points scored on August 1.
Cumulative Change in Score since August 1
Aug 2 Aug 3 Aug 4 Aug 5 Aug 6
The average cumulative change over the 6 days was
680−10−20+40+0​=690​=15 points
so Zelda's average score over the 6 days was 1700+15=(E)1715​ points.
The problems on this page are the property of the MAA's American Mathematics Competitions
