Step-3

Title: Averages

Grade: 8-a Lesson: S3-L2

Explanation: Let us verify the answer here with the steps.

Description:

Step Type Explanation Answer

1

Problem

The average of twelve positive numbers is 18. If the average of the first four numbers is 12 and that of the last four numbers is 30. What is the average of the remaining four numbers?

2

Hint

Formula used

\$"Average" = "Sum of set of numbers" / "Amount of numbers in set"\$

3

Step

Given that

Average of twelve positive numbers = 18

Average of the first four numbers = 12

Average of the last four numbers = 30

4

Step

Let

x be the average of the remaining numbers

5

Step

On Simplification

\$18 = (12 + x + 30)/3\$

6

Step

Multiplying 3 on both sides

\$18 \times 3 = \cancel3^1 \times (12 + x + 30)/\cancel3^1\$ ⇒ \$54 = x + 42\$

7

=

\$x = 54 - 42 = 12\$

8

Step

So, the average of the remaining numbers is

12


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