Answer:
1/6 ton of fish is fed during the feeding at night.
Step-by-step explanation:
The fish fed in the morning is [tex]\dfrac{2}{15}[/tex] tons, and during after noon the fish fed is [tex]\dfrac{1}{15}[/tex] more than in the morning; or
[tex]\dfrac{2}{15} +\dfrac{1}{15}[/tex]
and let us call the tons of fish fed at night [tex]x[/tex], then if the total tons of wish fed during the is [tex]\dfrac{1}{2}[/tex], we have
[tex]\dfrac{2}{15}+(\dfrac{2}{15} +\dfrac{1}{15})+x=\dfrac{1}{2}[/tex]
Let us add the numerators on the left side and we get:
[tex]\dfrac{5}{15} +x=\dfrac{1}{2}[/tex]
and subtract [tex]\dfrac{5}{15}[/tex] from both side to isolate [tex]x:[/tex]
[tex]x=\dfrac{1}{2} -\dfrac{5}{15}[/tex]
and since [tex]\dfrac{5}{15} =\dfrac{1}{3}[/tex], we have
[tex]x=\dfrac{1}{2}-\dfrac{1}{3}[/tex]
the common denominator of the fractions is 6; therefore, we rewrite the equation as
[tex]x=\dfrac{3}{6}-\dfrac{2}{6}[/tex]
and subtract the numerators to get:
[tex]\boxed{x=\dfrac{1}{6} }[/tex]
which the number of tons fed during the feeding at night.
