Answer :
SOLUTION
Step1
Define the parameters for the given information
[tex]\begin{gathered} \text{let} \\ A\text{lcohol content of solution A=x ml} \\ \text{ Alcohol content of solution B=y ml} \end{gathered}[/tex]Step2
Write out the equation for the information given
He uses twice as much solution A as solution B is written as
[tex]x=2y[/tex]Then
Solution A is 16% alcohol and solution B is 19% we have
[tex]\begin{gathered} \text{Solution A=}\frac{\text{16}}{100}x=0.16x \\ \text{Solution B=}\frac{\text{19}}{100}y=0.19y \end{gathered}[/tex]For the mixture to have 480ml of alcohol, we have
[tex]0.16x+0.19y=480[/tex]Step3
Solve the equation simultaneously
[tex]\begin{gathered} x=2y\ldots\ldots\text{.equation 1} \\ 0.16x+0.19y=480\ldots\ldots\text{equation 2} \end{gathered}[/tex]substitute equation (1) into equation (2)
we have
[tex]0.16(2y)+0.19y=480[/tex]expand the parenthesis
[tex]\begin{gathered} 0.32y+0.19y=480 \\ 0.51y=480 \\ divide\text{ both sides by 0}.51 \\ y=\frac{480}{0.51}=\frac{16000}{17} \end{gathered}[/tex]Then the value of becomes
[tex]\begin{gathered} x=2y \\ x=2\times\frac{16000}{17}=\frac{32000}{17} \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x=\frac{32000}{17} \\ \text{and } \\ y=\frac{16000}{17} \end{gathered}[/tex]Hence
Jose will needs 1882.35ml of solution A and 941.18ml of solution B
