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.

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

The average age of 27 kids = 7 years.

Total age of \$(27 "kids")/27\$ = 7

Multiply both sides by 27.

⇒ Total age of \$\cancel27^1 \times (27 "kids")/\cancel27^1\$ = \$7 \times 27\$

Total age of 27 kids = 189

If the teacher’s age is included, the average age becomes 10 years.

⇒ \$("Total age of 27 kids + Age of the teacher")/28 = 10\$

⇒ \$(189 + "Age of the teacher")/28 = 10\$

Multiply both sides by 28.

⇒ \$\cancel28^1 \times (189 + "Age of the teacher")/\cancel28^1 = 10 \times 28\$

⇒ 189 + Age of the teacher = 280

Subtract 189 from both sides.

⇒ \$\cancel189 + "Age of the teacher" - \cancel189 = 280 -189\$

Age of the teacher = 91 years