a chemist mixes a 10% hydrogen peroxide solution with a 25% hydrogen peroxide solution to create 30 liters…

a chemist mixes a 10% hydrogen peroxide solution with a 25% hydrogen peroxide solution to create 30 liters of a 15% hydrogen peroxide solution. how many liters of the 10% solution did the chemist use to make the 15% solution? liters

a chemist mixes a 10% hydrogen peroxide solution with a 25% hydrogen peroxide solution to create 30 liters of a 15% hydrogen peroxide solution. how many liters of the 10% solution did the chemist use to make the 15% solution? liters

Answer

Explanation:

Step1: Set up variables

Let $x$ be the volume of the 10% hydrogen - peroxide solution and $y$ be the volume of the 25% hydrogen - peroxide solution. We know two equations: $x + y=30$ (total volume) and $0.1x + 0.25y=0.15\times30$ (total amount of hydrogen - peroxide).

Step2: Express $y$ in terms of $x$ from the first equation

From $x + y=30$, we get $y = 30 - x$.

Step3: Substitute $y$ into the second equation

Substitute $y = 30 - x$ into $0.1x+0.25y = 0.15\times30$. We have $0.1x+0.25(30 - x)=4.5$.

Step4: Expand and solve for $x$

Expand the left - hand side: $0.1x + 7.5-0.25x=4.5$. Combine like terms: $0.1x-0.25x=4.5 - 7.5$. So, $-0.15x=-3$. Divide both sides by $- 0.15$: $x=\frac{-3}{-0.15}=20$.

Answer:

20