Question

Emma, who is the second-youngest, is 12 years old and has 7 members in her family. Her younger brother is 10 years old. The average age of her family is 25 years. Find the average age of the family just before Emma was born.

• A. 32.6 years
• B. 40.6 years
• C. 18.6 years
• D. 38.6 years

Answer 1

The correct option is C 18.6 years

Let the increasing order of ages of the family members be A1, A2, A3, A4, A5, A6, and A7, where A1 is the youngest and A7 is the oldest.

Emma is A2 = 12 years of age
A1 = 10 years of age

The average age of the family is 25 years.

$\frac{\text{A1 + A2 + A3 + A4 + A5 + A6 + A7}}{7}=25$

$A1+A2+A3+A4+A5+A6+A7=25\times 7$
$A1+A2+A3+A4+A5+A6+A7=175$

$10+12+A3+A4+A5+A6+A7=175$
$22+A3+A4+A5+A6+A7=175$
$A3+A4+A5+A6+A7=175–22$
$A3+A4+A5+A6+A7=153$

Before Emma was born,
$A1=0$
$A2=0$
Every other member is 12 years younger, and the family has 5 members.

Average age of the family
$=\frac{\text{A3 + A4 + A5 + A6 + A7}–12\times 5}{5}$
$=\frac{\text{A3 + A4 + A5 + A6 + A7}–60}{5}$
$=\frac{153–60}{5}$
$=\frac{\text{93}}{5}=18.6years$