Question

Theresa has 2 brothers and 1 sister whose ages are 12, 15, and 18 years old. If the mean age of all four siblings is 13, how old is Theresa A.5 B.7 C.9 D.11

Answer 1

B

1) Gathering the data

Theresa, Brother 1, Brother 2 and her Sister

Ages: 12 15 18

Mean: 13

2) We can find out Theresa's age by applying the Arithmetic Mean formula. There are four siblings, so 4 in the denominator. Let's call Theresa's age by "t" and replace x by 13 (the mean):

$\begin{gathered} x=\frac{t+12+15+18}{4} \\ 13=\frac{t+45}{4} \\ t+45=4\times13 \\ t=52-45 \\ t=7 \end{gathered}$

3) Hence, Theresa is 7 years old.