Respuesta :
Given:
First tank: 3% salt
Second tank : 10% salt
The fish requires 6% salt with a volume of 100 gallons
Let the required volume from the first tank be x.
Hence the required volume from the second tank would be:
[tex]=\text{ 100-x}[/tex]The amount of salt from the first tank plus the amount of salt from the second tank should be equal to the amount in the mixture:
[tex]\begin{gathered} x\text{ }\times\text{ 0.03 + \lparen100-x\rparen }\times\text{ 0.1 = 0.06 }\times\text{ 100} \\ 0.03x\text{ + 10 - 0.1x = 6} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 0.03x\text{ -0.1x = 6 - 10} \\ -0.07x\text{ = -4} \\ Divde\text{ both sides by -0.07} \\ x\text{ = 57.14 gallons} \end{gathered}[/tex]Hence the required volume of the first tank is 57.14 gallons. The volume of the second tank is:
[tex]\begin{gathered} =100\text{ - 57.14} \\ =\text{ 42.86 gallons} \end{gathered}[/tex]Answer:
We would required 57.14 gallons from the first tank and 42.86 gallons from the second tank
