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 60% acid solution? gabe needs liters of the 40% 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) and $0.4x + 0.7y=0.6\times60$ (acid - content equation).

Step2: Express $y$ in terms of $x$ from the total - volume equation

From $x + y=60$, we get $y = 60 - x$.

Step3: Substitute $y$ into the acid - content equation

Substitute $y = 60 - x$ into $0.4x+0.7y = 0.6\times60$. So $0.4x+0.7(60 - x)=36$.

Step4: Expand and solve for $x$

Expand: $0.4x + 42-0.7x=36$. Combine like terms: $0.4x-0.7x=36 - 42$, which gives $- 0.3x=-6$. Divide both sides by $-0.3$: $x=\frac{-6}{-0.3}=20$.

Answer:

20