Question

1. kyle is doing a chemistry experiment and has 30 ml of a 25% solution. how many ml of a 80% solution should he add to obtain a mixture that is a 50% solution?

	amount	%	total
solution 2	x	80	80x
mixture	x + 30	50	5(x + 30)

Explanation:

Step1: Set up equation based on mixture principle

The amount of pure substance before mixing equals the amount of pure substance after mixing. For the first - solution, the amount of pure substance is \(30\times0.25 = 7.5\). For the second - solution, the amount of pure substance is \(0.8x\). And for the mixture, the amount of pure substance is \(0.5(x + 30)\). So the equation is \(30\times0.25+0.8x=0.5(x + 30)\).

Step2: Expand and simplify the equation

\[

$$\begin{align*} 7.5+0.8x&=0.5x+15\\ 0.8x - 0.5x&=15 - 7.5 \end{align*}$$

\]

Step3: Solve for \(x\)

\[

$$\begin{align*} 0.3x&=7.5\\ x&=\frac{7.5}{0.3}\\ x& = 25 \end{align*}$$

\]

Answer:

25