How to calculate the complex fractional values with sum of numbers and letters in an equation

Question

Below is the equation. Not sure if I am doing the right thing but i can't seems to get the right value.

$$ \mathbf{1.6\over 121.8} = \frac { \mathbf{15\over M}} {\frac{15} M + {250\over 78} } $$

Find the value of $\mathbf M$.

If anyone has advice, would be appreciated

Answer 1

To start, combine the right side denominator to a single fraction denominator $78M.$ Then multiply top and bottom of right by $78M$ to get rid of one layer of fractions. Proceed...

Answer 2

invert both sides:$${121.8\over1.6}={{15\over M}+{250\over78}\over{15\over M}}$$ simpifly The LHS to ${609\over 8}$ and divide both sides by 15 over 15 ( aka 1) giving:$${609\over 8}={{1\over M}+{50\over 234}\over{1\over M}}$$ dividing by $1\over M$ is multiplying by M . This gives:$${609\over 8}=1+{50M\over234}$$ which implies:$$M={601\cdot 234\over400}={70317\over200}=351+{117\over200}$$

Answer 3

There are always many ways to solve equations like this. For example,

\begin{align} {609\over 8} &= {{1\over M}+{50\over 234}\over{1\over M}} \\ {609\over 8} &= 1 + {50M\over 234} \\ {50M\over 234} &= {601\over 8}\\ &\text{etc.} \end{align}