PROPORTIONS and MIXTURE
PROBLEMS
Created by Trudy Magennis
Let’s review! What are
proportions?
An equation in which two ratios are equal is
called a proportion
 A proportion can be written using colon
notation like this a : b :: c : d
 or as the more recognizable (and useable)
equivalence of two fractions. a/b = c/d

Proportions

In a proportion the product of the means
is equal to product of the extremes.
3 : 5 = 6 : 10
Means
Extremes
Proportions
3 6

5 10
Means
Extremes
6 x 5 = 3 x 10
30 = 30
Proportions
Determine if the following are proportions.
1)
5 60

3 36
Yes!
2)
8 4

15 8
No!
Proportions
5 60

3 36
8 4

15 8
3 x 60 = 5 x 36
4 x 15 = 8 x 8
180 = 180
Yes, it is a proportion.
60
 64
No, it is not a proportion.
Solving Proportions

4 = 24
y 30
4(30) = 24y
120 = 24y
120 = 24y
24 24
5=y

1. Cross Multiply

2. Solve for the
variable.
Solving Proportions

10 = 5
y 8
8(10) = 5y
80 = 5y
80 = 5y
5 5
16 = y
1. Cross Multiply
 2. Solve for the
variable

Try one on your own…

3 = 12
y
28
Correct! 7
And another…

6 = 12
n
24
Correct! 12
Proportions

Recall that a fraction is always used for part-towhole comparison, but a ratio can be used for
– part-to-part comparison
– part-to-whole comparison
– other comparisons such as length-to-width.
Practical Examples of mixtures

A proportion is a statement that two given ratios are
equal

Practical examples:
– If a punch recipe calls for 1 part of 7-up and 2 parts of
orange juice, then you need to use the same ratio (no
matter how much of punch you want) in order to keep
the taste consistent.
– If you are mixing paint to paint your house, you need
to keep the ratio (of color pigments to white paint)
constant to ensure that the color will remain exactly
the same.
Mixture Word Problems

A muffin recipe calls for 7 cups
flour for every 2 cups milk. How
much flour will you need if you
use 5 cups milk?
–First set up a proportion then solve for your
variable.
–Remember proportions are two equivalent ratios
set equal to each other.
–7 cups flour = x cups flour
2 cups milk
5 cups milk
Solving the proportion
7 cups flour = x cups flour
2 cups milk
5 cups milk
 7(5) = 2x
 35 = 2x
 35 = 2x
2
2
 17.5 = x
 You must use 17.5 cups of flour with 5
cups of milk!

Mixture Word Problems
– To make a certain concentration of a chemical, a
scientist mixes 81 ml of the chemical with 180
ml of distilled water. To make more of this
chemical concentration, exactly how many
milliliters of the chemical should the scientist
mix with 260 ml of distilled water?
– First set up a proportion, then solve for the variable.
– Remember proportions are two equivalent ratios set equal
to each other.
– 81ml chemical = x ml chemical
180 ml water 260 ml water
Solving the proportion
81ml chemical = x ml chemical
180 ml water
260 ml water
81(260) = 180x
21060 = 180x
21060 = 180x
180
180
117 ml chemical = x
Try one on your own…

Sandy mixes 8 ounces of cream
cheese with 12 ounces of salsa to
make a dip for her party. She
wants to use this mixture to make
48 ounces of dip. Exactly how
many ounces of cream cheese
should she use?
• First set up a proportion then solve for your variable.
• Remember proportions are two equivalent ratios
set equal to each other.
And another…

Heath mixes gasoline and oil to make
fuel for his motorbike. He adds 16 fluid
ounces of oil for every 2 gallons of
gasoline. Exactly how many fluid
ounces of oil does Heath need to add to
3 ¼ gallons of gasoline to make this
fuel?
In your journals, explain in words how
you would solve the following problem.

Joseph is mixing cleaning solution
with water to clean his kitchen floor.
He should use 1 fluid ounce of
cleaning solution for every ½ gallon
of water. If Joseph fills a bucket
with 4 ½ gallons of water, exactly
how many fluid ounces of cleaning
solution should he use?
Now, let’s do some more
practicing!