Question

How many gallons of \[3\%\] acid solution must be mixed with 60 gallons of \[10\%\] acid solution to obtain an acid solution that is \[8\%\]?

Answer 1

Hint: In this problem, we have to find the quantity of gallons of \[3\%\] acid solution that must be mixed with 60 gallons of \[10\%\] acid solution to obtain an acid solution that is \[8\%\]. We can first assume the quantity of gallons as x, we can then form an equation, where the unknown quantity of gallons and the acid solution are added to the given quantity of gallon and the acid solution, which will be equal to the given percentage of acid solution and the addition of gallons. We can solve this equation to get the answer.

Complete step by step solution:
We know that we have to find the quantity of gallons of \[3\%\] acid solution mixed with 60 gallons of \[10\%\] acid solution to obtain an acid solution that is \[8\%\].
We can now assume x as the unknown quantity of gallon.
We can now form an equation, where the unknown quantity of gallons and the acid solution are added to the given quantity of gallon and the acid solution, which will be equal to the given percentage of acid solution and the addition of gallons.
We can write it as,
\[\Rightarrow 3\%x+60\left( 10\% \right)=8\%\left( x+60 \right)\]
We can now convert the percentage to decimal form, we get
\[\Rightarrow 0.03x+60\left( 0.01\% \right)=0.08\%\left( x+60 \right)\]
We can now simplify the above step, we get
\[\begin{align}
  & \Rightarrow 0.05x=1.2 \\
 & \Rightarrow x=\dfrac{120}{5}=24 \\
\end{align}\]
Therefore, 24 gallons of \[3\%\] acid solution must be mixed with 60 gallons of \[10\%\] acid solution to obtain an acid solution that is \[8\%\] .

Note: Students make mistakes while converting the given percentage into its decimal form, where we divide the given percent number by 100, to convert it. We should also know how to form an equation from the given data and simplify it to get the value of the unknown data.