Lesson Example Discussion Quiz: Class Homework |
Step-1 |
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 27 kids is 7 years. If the teacher’s age is included, the average age becomes 10 years. Find the teacher’s age. |
|
2 |
Hint |
Formula used |
\$"Average" = "sum of set of numbers" / "amount of numbers in set"\$ |
3 |
Step |
The average age of 27 kids |
7 years |
4 |
Step |
According to the formula |
\$("Total age of 27 kids")/27\$ = 7 |
5 |
Step |
Multiply both sides by 27 |
⇒ \$\cancel27^1 \times ("Total age of 27 kids")/\cancel27^1\$ ⇒ \$7 \times 27\$ ⇒ \$189\$ |
6 |
Step |
Total age of 27 kids is |
189 |
7 |
Step |
If the teacher’s age is included, the average age becomes 10 years On Simplification |
\$("Total age of 27 kids + Age of the teacher")/28 = 10\$ ⇒ \$(189 + "Age of the teacher")/28 =\$ 10 |
8 |
Step |
Multiply both sides by 28 |
\$\cancel28^1 \times (189 + "Age of the teacher")/\cancel28^1 = 10 \times 28\$ |
9 |
Step |
On Cancelation |
189 + Age of the teacher = 280 |
10 |
Step |
Subtract 189 from both sides |
\$\cancel189 + "Age of the teacher" - \cancel189 = 280 -189\$ |
11 |
Step |
Age of the teacher is |
91 years |
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