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

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(1)/(3)+(5)/(6)+1(1)/(2)+(2)/(3) \\ (4)/(3)+(5)/(6)+(3)/(2)+(2)/(3) \\ \end{gathered}`

Take the LCM of the denominators, we have

`\begin{gathered} (4)/(3)+(5)/(6)+(3)/(2)+(2)/(3) \\ \\ (8+5+9+4)/(6)=(26)/(6)=(13)/(3) \end{gathered}`

Hence the total gallons of water drank is

`(13)/(3)=4(1)/(3)\text{gallons}`

The amount of gallons left will be

`\begin{gathered} 4(5)/(6)-4(1)/(3) \\ \text{Hence } \\ (29)/(6)-(13)/(3) \\ (29-26)/(6)=(3)/(6)=(1)/(2) \end{gathered}`

Therefore

`(1)/(2)\text{gallons of water left}`

Answer= 1/2 gallons of water left