Question

gabe amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. how many liters of each does he need to make the needed 60 liters of 60% acid solution? gabe needs 20 liters of the 40% solution. he also needs liters of the 70% solution.

Explanation:

Step1: Set up variables

Let $x$ be the volume of the 40% solution and $y$ be the volume of the 70% solution. We know that $x + y=60$ (total volume equation), so $x = 60 - y$.

Step2: Set up acid - content equation

The amount of acid in the 40% solution is $0.4x$, in the 70% solution is $0.7y$, and in the final 60 - liter 60% solution is $0.6\times60 = 36$. So, $0.4x+0.7y=36$.

Step3: Substitute $x$ into acid - content equation

Substitute $x = 60 - y$ into $0.4x+0.7y=36$:
$0.4(60 - y)+0.7y=36$.
Expand: $24-0.4y + 0.7y=36$.
Combine like - terms: $24 + 0.3y=36$.

Step4: Solve for $y$

Subtract 24 from both sides: $0.3y=36 - 24=12$.
Divide both sides by 0.3: $y=\frac{12}{0.3}=40$.

Answer:

40