Word Problem

Question

A solution is 10% citric acid. if 3 liters of a 20% citric acid solution are added to it, the result is a solution this is in a ratio of 13 parts citric acid to 102 parts "other than citric acid". How many total liters were in the original solution (before 3 L were added)?

 

 

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up an algebraic expression that relates the variables to one another! On this one we have

Total citric acid: 0.10V + 0.6

Total “other”: 0.90V + 2.4

And then we know that the end ratio is 13/102.

Combining that into a full equation yields

(0.10V + 0.6) / (0.90V + 2.4) = 13/102

Then solving that algebraically for the value of “V” yields

102(0.10V + 0.6) = 13(0.90V + 2.4)

10.2V + 61.2 = 11.7V +31.2

30 = 1.5V

V = 30/1.5 = 20

Which means that the original salutation contained 20 liters

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

x = liters of original 10% citric acid.

 

3(20%) + x(10%) = liters citric acid

 

3 + x = total liters

 

(3(20%) + x(10%)) / (3 + x) = 13 / (102 + 13)

 

13(3 + x) = 115(3(20%) + x(10%))

 

39 + 13x = 115(3/5 + x/10)

 

39 + 13x = 23(3) + 11.5x

 

1.5x = 30

 

x = 300/15

 

x = 20 liters