Answer
$10$ milliliters of $34\%$.
$90$ milliliters of $4\%$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the first quantity with $34\%$ silver nitrate be $=x$.
Let the second quantity with $4\%$ silver nitrate be $=y$.
Step 2:- Write the system of equations.
$34\%$ of the first quantity is $0.34x$.
$4\%$ of the second quantity is $0.04y$.
$7\%$ of the required quantity is $0.07\times 100 = 7$ milliliters.
The given values are
Total quantity $= \$100$ milliliters.
Total quantity of silver nitrate $=7$ milliliters.
Or we can write.
$\Rightarrow x+y=100$ ...... (1)
$\Rightarrow 0.34x+0.04y=7$ ...... (2)
Step 3:- Solve the system of equations.
Multiply equation (1) by $-0.34$.
$\Rightarrow -0.34x-0.34y=-34$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.34x+0.04y-0.34x-0.34y=7-34$
Simplify.
$\Rightarrow -0.30y=-27$
Divide both sides by $-0.30$.
$\Rightarrow \frac{-0.30y}{-0.30}=\frac{-27}{-0.30}$
Simplify.
$\Rightarrow y=90$
Plug the value of $y$ into equation (1).
$\Rightarrow x+90=100$
Isolate $x$.
$\Rightarrow x=100-90$
Simplify.
$\Rightarrow x=10$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (1).
$\Rightarrow 10+90=100$
$\Rightarrow 100=100$ True.
