Hello there. To solve this question, we'll have to remember some properties about percentages.
Given that a chemist mixes 500 mililiters of a solution that is 62% acid with 125 mililiters of a solution that is 27% acid, we have to determine:
a) How many mililiters of acid are in the resulting mixture?
For this, we find how much is 62% of 500 and 27% of 125, adding the results.
62% of 500 can be calculated by multiplying:
[tex]\frac{62}{100}\cdot500=62\cdot5=310\text{ ml}[/tex]
And 27% of 125 is calculated as:
[tex]\frac{27}{100}\cdot125=\frac{27}{4}\cdot5=27\cdot1.25=33.75\text{ ml}[/tex]
Adding the results, we have
[tex]343.75\text{ ml}[/tex]
worth of acid in the mixture.
b) What percentage of the resulting mixture is acid?
For this, we find how many ml there are in the solution by adding:
[tex]500+125=625[/tex]
Now, we take the ratio between the amount of acid in the mixture we found in the last step and this number
[tex]\frac{343.75}{625}=0.55[/tex]
Multiplying by 100%, we get
[tex]0.55\cdot100\%=55\%[/tex]
This is the result we were looking for.
