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Mathematics
OpenStudy (anonymous):

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?

OpenStudy (shadowfiend):

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?

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

Great!

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