What is the value of s in the equation 1/2 + 2/5s = s - 3/4?

[EngineerJay]

Hey everyone was having trouble solving this on Khan academy. The way they got the answer made no sense what so ever so hoping anyone here can help.

If 1/2 + 2/5s = s - 3/4, what is the value of s?

 

[soroban]

$$\text{Solve for }s:\;\;\tfrac{1}{2} + \tfrac{2}{5}s \;=\; s - \tfrac{3}{4}$$

$$\begin{array}{ccc}\text{Multiply by 20:} & 10 + 8s \;=\;20s - 15 \\<br /> \text{Simplify:} & 12s \;=\;25 \\<br /> \text{Therefore:} & s \;=\;\frac{25}{12}<br /> \end{array}$$

 

[EngineerJay]

Okay so why did you multiply by 20? And how exactly?

 

[Greg]

Since 20 is the least common multiple of 2, 4 and 5, multiplying by 20 clears away the denominators of the fractions, like this:

$$\dfrac12 + \dfrac{2}{5}s = s - \dfrac34$$

Multiply each side by 20:

$$20\left(\dfrac12 + \dfrac{2}{5}s\right) = 20\left(s - \dfrac34\right)$$

Expand:

$$20\cdot\dfrac12 + 20\cdot\dfrac{2}{5}s = 20s - 20\cdot\dfrac34$$

Evaluate:

$$10+8s=20s-15\implies s=\dfrac{25}{12}$$

 

[EngineerJay]

Wow thanks for the help! Now that I know I should of found the lcm of 2, 4 and 5 I feel some type of way(Giggle)! Again Thank you.