Question

Clayton will mix xxx milliliters of a 10\%10%10, percent by mass saline solution with yyy milliliters of a 20\%20%20, percent by mass saline solution in order to create an 18\%18%18, percent by mass saline solution. The equation above represents this situation. If Clayton uses 100100100 milliliters of the 20\%20%20, percent by mass saline solution, how many milliliters of the 10\%10%10, percent by mass saline solution must he use?

Answer 1

Answer:

25 mL of the 10% solution.

Explanation:

Clayton will mix x milliliters of a 10%, percent by mass saline solution with y milliliters of a 20%, percent by mass saline solution in order to create an 18%, percent by mass saline solution. This can be described with the following equation:

0.1 x + 0.2 y = 0.18 (x + y)   [1]

If Clayton uses 100 milliliters of the 20%, percent by mass saline solution, how many milliliters of the 10%, percent by mass saline solution must he use?

If y = 100 mL, what should be the value of x?

Let's solve [1] for "x" and replace with the value of "y".

0.1 x + 0.2 y = 0.18 (x + y)

0.1 x + 0.2 y = 0.18 x + 0.18 y

0.02 y = 0.08 x

x = 0.25 y = 0.25 × 100 mL = 25 mL