Given:
- A 10% acid solution.
- A 80% acid solution.
You need to produce 70 liters of a 65% acid solution.
Let be "t" the number of liters of 10% acid solution that must be used, and "g" the number of liters of 80% acid solution that must be used to produce 70 liters of a 65% acid solution.
By definition, you know that:
[tex]10\text{ \%}=\frac{10}{100}=0.1[/tex][tex]80\text{ \%}=\frac{80}{100}=0.8[/tex][tex]65\text{ \%}=\frac{65}{100}=0.65[/tex]
Therefore, you can set up the following System of Equations using the data provided in the exercise:
[tex]\begin{cases}0.1t+0.8g=0.65(70){} \\ t+g=70{}\end{cases}[/tex]
Use the Substitution Method to solve it:
1. Solve the second equation for "t":
[tex]t=70-g[/tex]
2. Substitute it into the first equation and solve for "g":
[tex]0.1(70-g)+0.8g=45.5[/tex][tex]\begin{gathered} 7-0.1g+0.8g=45.5 \\ 0.7g=45.5-7 \\ \\ g=\frac{38.5}{0.7} \\ \\ g=55 \end{gathered}[/tex]
3. Substitute the value of "g" into this equation and then evaluate:
[tex]t=70-g[/tex]
Then:
[tex]\begin{gathered} t=70-55 \\ t=15 \end{gathered}[/tex]
Hence, the answer is:
• 15 liters of 10% acid solution.
,
• 55 liters of 80% acid solution.
