Percent Mixture Problems
Written by Dr. Ed D’Souza, Rialto Unified School District
Using the tug-of-war approach, imagine the white jelly beans having a tug-of-war
game with the blue jelly beans. Both want the final price to be closer to their price.
METHOD 2:Teeter-Totter Method
White jelly beans cost $0.25 a pound and blue jelly beans cost $0.85 a
pound. How many pounds of white jelly beans must be added to 25
pounds of blue jelly beans to arrive at a mixture worth $0.45 a pound?
1. Draw a "rope" (straight line) and label the three numbers you know.
W=25
M =45
B= 85
2. The left point on the rope is the price of the white jelly beans (25), the right
point is the price of the blue jelly beans (85), and the "fulcrum" will be
located at the final price (45), and closer to the left side. Try to approximate
where 45 would land between 25 and 85.
Price (cents) W= 25
M= 45
B= 85
3. Label what you know - the pull to the right is 25. Label what you don't know
the pull to the left is x.
4.
Amount (lbs)
Price(cents)
Amount (lbs)
20
W= 25
x
40
M=45
B= 85
25
5. Calculate the gap in price between the knot and the left side (20cents) and
between the knot and the right side (40 cents- see bullet 3.). Since the gap on the
left is half as big, the left side must be pulling twice as hard. Therefore, we must
have 50 pounds of white jelly beans.
Students will eventually discover the rule: (gap) x (pull) = (gap) x (pull). Multiply
the gap on the left (20) by the pull to the left (the unknown). Set this quantity to the
gap on the right (40) times the pull to the right (25). Solving for the unknown
yields 50 pounds.
(20)(x) = (40)(25)
x
= (40)(25) = 50lbs
20
So , 50 lbs of white jelly beans need to be added to the mixture.
Mixtures –Finding the Balance
1.
Coffee
Cost
$3/lb
$3.25/lb
$3.50/lb
Mixture
5lbs
x lbs
2.
Butterfat
%
2%
6.4%
8.4%
Mixture
x liters
3.
1 liter
Grape juice
%
15%
20%
100%
Mixture
800ml
x mL
MIXTURE PROBLEMS
THE JELLY BEAN PROBLEM
White jelly beans cost $0.25 a pound and blue jelly beans cost $0.85 a pound. How
many pounds of white jelly beans must be added to 25 pounds of blue jelly beans to
arrive at a mixture worth $0.45 a pound?
SALT SOLUTION
A mixture containing 6% salt is to be mixed with 2 ounces of a mixture which is
15% salt, in obtaining a solution which is 12% salt. How much of the first solution
must be used?
A SOLUTION
How many liters of a 70% acid solution must be added to 50 liters of a 40% acid
solution to produce a 50% acid solution?
COFFEE ANYONE?
Find the selling price per pound of a coffee mixture made from 8 pounds of coffee
that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound.
A VEGETABLE MEDLEY
How many pounds of lima beans that cost $0.90 per pound must be mixed with 16
pounds of corn that costs $0.50 per pound to make a mixture of vegetables that
costs $0.65 per pound?
A LITE PUNCH
Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 L of
another punch. The resulting fruit punch is 20% fruit juice. Find the percent of
fruit juice in the 300 liters of punch.
THE CEREAL PROBLEM
Ten grams of sugar are added to a 40-g serving of a breakfast cereal that is 30%
sugar. What is the percent concentration of sugar in the resulting mixture?
How many liters of water must be added to 50 L of 30% acid solution in
order to produce a 20% acid solution?