Solving Mixture Word ProblemsAug. 11th, 2014

What is a solution?• A solution is a mixture of one substance dissolved in another

so the properties are the same throughout. • For our examples we will be mixing different concentrations

of solutions in order to obtain a specific concentration that we do not have.

Example 1How many ounces of a 30% solution should Jane mix with 40 ounces of a 60% solution to make a 35% solution?

% (in decimals) ounces

.3 x .3x

.6 40 .6(40)

.35 x+40

Percentage we wish to obtain. .35(x + 40) = .3x + .6(40)

.35x + 14 = .3x + 24-.3x -.3x.05x + 14 = 24 -14 -14 .05x = 10 .05 .05

x = 200

*Multiply ACROSS*Add DOWN

Jane would need 200 ounces of 30% solution to make a 35% solution.

Example 2If you have 20 ounces of a 50% solution, how much must you add of a 20% solution to make a 45% solution?

% (in decimals) ounces

.5 20 .5(20)

.2 x .2x

.45 20 + x

.45(20 + x) = .5(20) + .2x 9 + .45x = 10 + .2x -.2x -.2x 9 + .25x = 10- 9 - 9 .25x = 1 .25 .25

x = 4You would need 4 ounces of 20% solution to make a 45% solution.

Example 3An exterminator has one tank containing a 50% water solution of poison and another tank that contains 30% solution of the same poison, How much of each solution must the worker mix to make 40 liters of a 35% solution?

% (in decimals) liters

.5 x .5x

.3 y .3y

.35 40

.35(40) = .5x + .3y 14 = .5x + .3y 14 = .5x + .3(40 – x) 14 = .5x + 12 - .3x 14 = .2x + 12 - 12 - 12 2 = .2x .2 .2

How much he wants to make total.

x + y = 40-x -x y = 40 - x

We now have 2 variables, so we need 2 equations.

Solve for a variable

Substitute to make a 1 variable equation

x = 10

What does that mean?

You need 10 liters of 50% solution. But what about the 30% solution?

Plug in 10 for x!

You need 30 liters of the 30% solution.

So all together: The worker needs 10 liters of 50% solution and 30 liters of 30% solution.

y = 40 - x

y = 40 – 10y = 30

Real Word Problems

Example 4If Jim can paint a house in 6 hours and James can paint the same house in 7 hours, how long will it take for them to paint to paint the house together?

Set up ratios

Find the common denominatorSimplify

Solve

13 13H = 3.23

It would take them 3.23 hours to paint the house together.

Example 5If Jasmine can detail a car in 3 hours and Carlos can detail the same type of car in 5 hours, how long will it take for them to detail the car together?

Set up ratios

Find the common denominatorSimplify

Solve

8 8C = 1.875

It would take them 1.875 hours to paint the house together.