A scientist wants to dilute a 60% acid solution by adding some 20% solution. If she starts with 80 ml of the 60% solution, how many milliliters of the 20% solution does she need to add to get a resulting 45% acid solution?
Solution
Let x be the amount of the 60% solution
Let y be the amount of the 20% solution
Let x + y be the amount of the mixture
60% of x solution + 20% of y solution = 45% of amount of mixture
We use 60% of the x solution or 60% of 80 ml.
60% of 80 = 0.60 times 80 = 48
We use 20% of the y solution or 20% of y
20% of y = 0.20 times y = 0.20y
The mixture is x + y and we need 45% of the mixture or
45% of (x + y)
45% of (x + y) = 0.45(x + y)
Putting it all together we get:
48 + 0.20y = 0.45(48 + y)
48 + 0.20y = 21.6 + 0.45y
48 - 21.6 = 0.45y - 0.20y
26.4 = 0.25y
y = 26.4 / 0.25 = 105.6
Indeed,
0.60 times 80 + 0.20 times 105.6 = 48 + 21.12 = 69.12
0.45 times (48 + 105.6) = 0.45 times 153.6 = 69.12
Jul 06, 18 12:29 PM
Learn how to solve two types of logarithmic equations
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Jul 06, 18 12:29 PM
Learn how to solve two types of logarithmic equations
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.