Answer :
Solution:
Let the number of ounces of solution A be
[tex]=x[/tex]Let the number of ounces of solution B be
[tex]=y[/tex]The total number of ounces of the mixture is
[tex]=180[/tex]Therefore,
The equation to represent this will be
[tex]x+y=180\ldots\ldots(1)[/tex]The percentage of salt in solution A is
[tex]\begin{gathered} =40\% \\ =\frac{40}{100}=0.4 \end{gathered}[/tex]The percentage of salt in solution B is
[tex]\begin{gathered} =55\% \\ =\frac{55}{100}=0.55 \end{gathered}[/tex]The percentage of salt in the mixture is
[tex]\begin{gathered} =45\% \\ =\frac{45}{100}=0.45 \end{gathered}[/tex]Therefore,
The equation to represent the percentage of salt is given below as
[tex]\begin{gathered} 0.4x+0.55y=0.45\times180 \\ 0.4x+0.55y=81 \\ \text{ multiply through by 100} \\ 40x+55y=8100\ldots\text{.}(2) \end{gathered}[/tex]Step 1:
From equation (1) make x the subject of the formula
[tex]\begin{gathered} x+y=180 \\ x=180-y\ldots\text{.}\mathrm{}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} 40x+55y=8100 \\ 40(180-y)+55y=8100 \\ 7200-40y+55y=8100 \\ 15y=8100-7200 \\ 15y=900 \\ \text{divide both sides by 15} \\ \frac{15y}{15}=\frac{900}{15} \\ y=60 \end{gathered}[/tex]Step 3:
Substitute y=60 in equation (3)
[tex]\begin{gathered} x=180-y \\ x=180-60 \\ x=120 \end{gathered}[/tex]Hence,
The number of ounces of solution A = 120
The number of ounces of solution B = 60
