Question

I need assistance solving this question without solving for x. I need help explaining how to solved by fraction methodological order only.

Answer 1

SOLUTION

Write out the given information

$\begin{gathered} \text{Total gallons of water=4 }\frac{\text{5}}{6} \\ \text{James drank=1 }\frac{\text{1}}{3}\text{gallons} \\ \text{Gilbert drank=}\frac{\text{5}}{6}\text{gallons} \\ \text{Mathew drank=1 }\frac{\text{1}}{2}\text{gallons} \\ \text{Simon drank=}\frac{\text{2}}{3}gallons\text{ } \end{gathered}$

To know the gallons of water left at the end of the day, we add all the gallons of water drank and subtract from the total gallons:

Hence, the sum is

$\begin{gathered} 1\frac{1}{3}+\frac{5}{6}+1\frac{1}{2}+\frac{2}{3} \\ \frac{4}{3}+\frac{5}{6}+\frac{3}{2}+\frac{2}{3} \\ \end{gathered}$

Take the LCM of the denominators, we have

$\begin{gathered} \frac{4}{3}+\frac{5}{6}+\frac{3}{2}+\frac{2}{3} \\ \\ \frac{8+5+9+4}{6}=\frac{26}{6}=\frac{13}{3} \end{gathered}$

Hence the total gallons of water drank is

$\frac{13}{3}=4\frac{1}{3}\text{gallons}$

The amount of gallons left will be

$\begin{gathered} 4\frac{5}{6}-4\frac{1}{3} \\ \text{Hence } \\ \frac{29}{6}-\frac{13}{3} \\ \frac{29-26}{6}=\frac{3}{6}=\frac{1}{2} \end{gathered}$

Therefore

$\frac{1}{2}\text{gallons of water left}$

Answer= 1/2 gallons of water left