word problem question

Question

Marty is a lab assistant for a chemistry instructor. The instructor needs 20 liters of a solution that is 15% alcohol. Marty has a solution that is 18% alcohol and a solution that is 10% alcohol. How many liters of each solution must Marty mix together to prepare the solution needed by the instructor?

18% solution:

10% solution:

Answer 1

a + b = 20 -----> a = 20 - b

18a + 10b = 15(20)

 

18(20 - b) + 10b = 300

360 - 18b + 10b = 300

8b = 60

b = 7.5

 

a = 20 - 7.5 = 12.5

 

Let's check.

 

18(12.5) + 10(7.5) = 300

225 + 75 = 300

 

Good thing I checked my answer, because I did it wrong the first time!

Answer 2

x represents the amount 18%

20 - x represents the amount of 10%

 

0.18x + 0.20(20 - x) = 0.15(20)

 

Can you solve for x?