2005 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

The average (mean) of

20

numbers is

30,

and the average of

30

other numbers is

20.

What is the average of all

50

numbers?

Show solution

Solution

The total of all

50

numbers is

20 \cdot 30 + 30 \cdot 20

= 600 + 600

= 1200.

The average is

1200 \div 50 = 24.

Thus, the correct answer is B.

Concepts: mean

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.