Problem:
The table below gives the percent of students in each grade at Annville and Cleona elementary schools:
Annville:Cleona:​K​16%12%​1​15%15%​2​15%14%​3​14%13%​4​13%15%​5​16%14%​6​11%17%​
Annville has 100 students and Cleona has 200 students. In the two schools combined, what percent of the students are in grade 6?
Answer Choices:
A. 12%
B. 13%
C. 14%
D. 15%
E. 28%
Solution:
In Annville 11% of 100, or 11 students are in the 6th grade. In Cleona 17% of 200, or 34 students are in the 6th grade. Thus in the two schools combined, 45 out of 300 students are in the 6th grade, so 45/300=0.15=15% of all the students are in the 6th grade.
OR
Since 1/3 of the students are at Annville and 2/3 are at Cleona, using a weighted average yields 31​(0.11)+32​(0.17)=0.15 or 15%.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions