Answer:
The container can hold 24 gallons of water.
Step-by-step explanation:
Let the Amount of water in gallons container can hold be 'x'.
Now given:
the container that holds the water for the football team is 1/4 full.
therefore Amount of water in container = [tex]\frac14x[/tex]
We need to find the Amount of water in gallons container can hold.
Solution:
Now given:
after pouring in 10 gallons of water, it is 2/3 full.
So equation can be framed as;
[tex]\frac14x+10=\frac23x[/tex]
Now Combining the like terms we get;
[tex]10=\frac23x-\frac14x[/tex]
Now We will use LCM to make the denominator common we get;
[tex]10=\frac{2x\times4}{3\times4}-\frac{1x\times3}{4\times3}\\\\10=\frac{8x}{12}-\frac{3x}{12}[/tex]
Now the denominators are common so we will solve the numerator we get;
[tex]10=\frac{8x-3x}{12}\\\\10=\frac{5x}{12}[/tex]
Now Multiplying both side by [tex]\frac{8}{12}[/tex] we get;
[tex]10\times\frac{12}{5}=\frac{5x}{12}\times \frac{12}{5}\\\\x=24 \ gallons[/tex]
Hence The container can hold 24 gallons of water.
