Problem Solving

BTGmoderatorDC wrote:Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will be twice as old as Candice. If, 4 years from now, Abigail will be 36 years old, how old will Candice be in 6 years?

A. 5
B. 6
C. 7
D. 8
E. 9

OA C

Source: Manhattan Prep

Let the age of Bonnie \(= x\)
\(\Rightarrow\) Age of Abigail \(= 4x\) and Candice \(= C\)

\(\begin{array}{|c|c|c|c|}
\hline
A & B & C & \textrm{Time} \\ \hline
4x & x & C & \textrm{Present} \\ \hline
4x+6 & x+6 & C+6 & \textrm{After $6$ years} \\ \hline
4x+4 & x+4 & C+4 & \textrm{After $4$ years}\\ \hline
\end{array}\)

Given,
In 6 years, Bonnie will be twice as old as Candice
\(\Rightarrow x+6 = 2(C+6)\)
\(\Rightarrow C = \frac{x}{2} - 3\)

4 years from now, Abigail will be 36 years old
\(\Rightarrow 4x+4 = 36\).
\(\Rightarrow x = 8 \)
\(\Rightarrow C = \frac{8}{2} - 3 = 1\)

In 6 years, age of Candice \(= 1 + 6 = 7\)

Therefore, option __C__