Question

At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12,$ $15,$ and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

$12$

$\dfrac{37}{3}$

$\dfrac{88}{7}$

$13$

$14$

Answer: C

Concepts:weighted mean ratio and proportion

Difficulty rating: 1040

Solution:

Take the grade sizes in the ratio $4 : 2 : 1$ for third, fourth, and fifth grades. The weighted average is $\begin{aligned} \dfrac{4\cdot12+2\cdot15+10}{7} \\ = \dfrac{48+30+10}{7} \\ = \dfrac{88}{7}. \end{aligned}$

Thus, the correct answer is C.

2011 AMC 12A Problem 4

Answer: C

Difficulty rating: 1040

Solution:

Problem 4 in Other Years