Question

1. katie is doing a chemistry experiment and has 50 ml of a 25% solution. how many ml of a 70% solution should she add to obtain a mixture that is a 30% solution?

	amount	%	total
solution 1	50ml	25
solution 2
mixture		30

Explanation:

Step1: Set up the equation

Let $x$ be the volume (in ml) of the 70% solution. The amount of solute in Solution 1 is $0.25\times50$, the amount of solute in Solution 2 is $0.7x$, and the amount of solute in the mixture is $0.3\times(50 + x)$. So the equation is $0.25\times50+0.7x=0.3\times(50 + x)$.

Step2: Expand and simplify the equation

First, calculate $0.25\times50 = 12.5$ and $0.3\times(50 + x)=15+0.3x$. The equation becomes $12.5 + 0.7x=15+0.3x$.

Step3: Solve for $x$

Subtract $0.3x$ from both sides: $12.5 + 0.7x-0.3x=15+0.3x - 0.3x$, which simplifies to $12.5 + 0.4x=15$. Then subtract 12.5 from both sides: $0.4x=15 - 12.5$, so $0.4x = 2.5$. Divide both sides by 0.4: $x=\frac{2.5}{0.4}=6.25$.

Answer:

$6.25$ ml