Averages Complex Examples 1

In this class, We discuss Averages Complex Examples 1.

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Example 1:

The average age of students in a class is 15.8 years.

The average age of boys in the class is 16.4 years, and girls are 15.4 years.

What is the ratio of the number of boys to that of girls?

Solution:

Let the ratio of boys to girls is K: 1

Why K: 1? why not x: y?

Example: 2:5 can be written as 2/5: 1.

By taking K: 1, we have the flexibility to solve a single variable.

(K * 16.4 + 1 * 15.4) = (K+1) * 15.8

(16.4 – 15.8)K = 15.8 – 15.4

K = 0.4/0.6

K = 2/3

Ratio = 2/3 : 1 = 2:3

Example 2:

The arithmetic mean of the scores of a group of students in a test is 52.

The brightest 20 percent secured a mean score of 80, and the dullest 25 percent secured a mean score of 31.

The mean of the remaining 55 percent?

Solution:

Number of students = y

Mean of 55 percent = x

0.2y* 80 + 0.25y *31 + 0.55y * x = 52y

2*80 + 25*31 + 55 *x = 52 * 100

x = 565/11 = 51.4