Question

A class of 25 students took a math test. Ten students had an average of 88. The other students had an average of 76. What is the average of the whole class?
A) 78.2
B) 80.8
C) 81.7
D) 82.5

Answer 1

The answer is B. 80.8

Answer 2

Answer:

The average of the whole class is 80.8.

The correct answer is B)

Step-by-step explanation:

To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.

Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.

$average=\frac{80+89+95}{3}=\frac{264}{3}=88$

The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.

$average=\frac{88+88+88}{3}=\frac{264}{3}=88$

The previous expression could be simplified as:

$average=\frac{88\times 3}{3}$

Where, the number 3 means the number of students.

With that in mind, the phrase "Ten students had an average of 88" could be written as:

$average_{10\, \, students}=\frac{88+88+88+88+88+88+88+88+88+88}{10}$

$average_{10\, \, students}=\frac{88\times 10}{10}=88$

On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:

$average_{15\, \, students}=\frac{76+76+76+76+76+76+76+76+76+76+76+76+76+76+76}{15}$

$average_{15\, \, students}=\frac{76\times 15}{15}=76$

Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals $88\times 10+76\times 15$. The total number of scores would be: 25.

$average_{total}=\frac{88\times 10 + 76\times 15}{25}$

$average_{total}=\frac{880 + 1140}{25}$

$average_{total}=\frac{880 + 1140}{25}$

$average_{total}=\frac{2020}{25}$

$average_{total}=80.8$

Thus, the average of the whole class is 80.8. The correct answer is B)