Question

can anyone help me on this problem? "Mary's age is twice Fred's age and 1/3 of Sally's age. If the sum of their ages is 99 how old are they?

Answer 1

Let's call Mary's age \(m\), Fred's age \(f\), and Sally's age \(s\). Then:

\[\begin{align}
m &= 2f\\
m &= \frac{s}{3}\\
m + s + f &= 99
\end{align}\]

We can solve this system of equations first by solving for \(s\) in terms of \(m\):

\[s = 3m\]

We already have \(m\) in terms of \(f\), which means we have \(s\) in terms of \(f\) as well: \(s = 3m = 3(2f) = 6f\). So we can plug into the last equation to solve for \(f\):

\[\begin{align}
2f + 6f + f &= 99\\
9f &= 99\\
f &= 11
\end{align}\]

Is this enough for you to find the other ages?

Answer 2

oh my goodness yes i think that helps SO much! THANK YOU!!!

Answer 3

Great!