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Title: Averages

Grade: 8-a Lesson: S3-L1

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

Description:

Step	Type	Explanation	Answer
1	Problem	The average age of the mother and her two sons is 40 years and that of two sons is 30 years. Find the mother’s age?
2	Hint	Formula used	\$"Average" = "sum of set of numbers" / "amount of numbers in set"\$
3	Step	The average age of the mother and her two sons	40 years
4	Step	According to the formula	\$"Sum of their ages"/3 \$ = 40
5	Step	Multiply with 3 on both sides	\$\cancel3^1 \times ("Sum of their ages")/\cancel3^1 = 40 \times 3\$
6	Step	Sum of their ages	120 years
7	Step	The average age of two sons	30 years
8	Step	According to the formula	\$"Sum of the ages of two sons"/2 \$ = 30
9	Step	Multiply with 2 on both sides	\$\cancel2^1 \times ("Sum of the ages of two sons")/\cancel2^1 = 30 \times2\$
10	Step	Sum of their ages	60 years
11	Step	Mother’s age	120 - 60 = 60 years
12	Step	Therefore, the mother’s age	60 years

Step

Type

Explanation

Answer

Problem

The average age of the mother and her two sons is 40 years and that of two sons is 30 years. Find the mother’s age?

Hint

Formula used

\$"Average" = "sum of set of numbers" / "amount of numbers in set"\$

Step

The average age of the mother and her two sons

40 years

Step

According to the formula

\$"Sum of their ages"/3 \$ = 40

Step

Multiply with 3 on both sides

\$\cancel3^1 \times ("Sum of their ages")/\cancel3^1 = 40 \times 3\$

Step

Sum of their ages

120 years

Step

The average age of two sons

30 years

Step

According to the formula

\$"Sum of the ages of two sons"/2 \$ = 30

Step

Multiply with 2 on both sides

\$\cancel2^1 \times ("Sum of the ages of two sons")/\cancel2^1 = 30 \times2\$

Step

Sum of their ages

60 years

Step

Mother’s age

120 - 60 = 60 years

Step

Therefore, the mother’s age

60 years