About this
Daily Classroom Special
M & M - Math and Mixture Problems was written by Nancy Powell,
teacher at Bloomington High School, Bloomington (IL) and former Teachers
Network web mentor.
Subject:
Algebra I Materials
Needed: One box of snack size m&m minis for each student
Optional (virtual) field trip: the m&m's website at: http://m-ms.com/
The Mars candy
company was getting ready to introduce the blue M&M. In their marketing
meeting, they began to explore pricing for its new promotion. If brown
M&M's cost $.25 per pound and blue M&M's cost $.85 per pound, how
many pounds of brown M&M's must be added to 300 lbs. of blue M&M's
to obtain a mixture that would sell for $.45 per pound? Before answering
this question, think about these questions and answer them first.
-
If 300 lbs.
of brown M&M's were added to the 300 lbs of blue M&M's, how
much should each lb. cost? Why?
-
Should the
company add more or less than 300 lbs. of brown M&M's to reach
their target price per pound? Why?
-
If the company
added 600 pounds of brown M&M's to the blue ones, what should
the cost of one pound of the mixture be? Why?
Let's take a
look at this problem like a tug of war....
-
First, draw
a rope (a straight line) and label the three numbers that you
know. The left end of the rope is the price of the brown M&M's
which is $.25. The right end of the rope is the price of the
blue M&M's which is $.85. The flag on the rope will be located
at the final price of the new brown/blue mixture ($.45).
-
Draw arrows
to show the pulling force in each direction. Since the brown
M&M's are pulling harder ($.45 is closer to $.25 than it is
to $.85) then make the left arrow longer than the arrow pointing
to the right.
-
Label what
you know about the amount of pull each mixture has...the pull
to the right is 300 lbs. and let the pull to the left be B since
you don't know how many brown M&M's to add.
-
Calculate
the gap between the flag and the left side ($.20) and between
the flag and the right side ($.40). Since the gap on the left
is half as big, the left side must be pulling twice as hard.
Therefore, we must need 600 pounds of brown M&M's to correctly
make the mixture.
-
Notice that
the gap times the amount of pull on the left = the gap times
the amount of pull on the right (.20)(x) = (.40)(300).
Let's try
another...
Another mixture
is being contemplated by the M&M marketing team. This mixture contains
the remaining Valentine's mixture that is 40% red. The marketing
team wants to change it to 88% red. If they have 100 pounds of the
Valentine mixture and a new batch of red M&M's, how many pounds
of the red M&M's must be added to the existing mixture? (Draw a
diagram!)
The people that
make the dyes to color the M&M's have to mix the colors very carefully
so that all of the M&M's match exactly. At the end of one batch
of orange dye, the person in charge of making more orange found
that she had 50 liters of red dye left. She knows that to make that
perfect shade of orange that she will need to have 55% of the final
mixture red dye and 45% should be yellow dye. How much yellow dye
should she add to the 50 liters of red dye if she is to make the
perfect M&M orange?
After Valentine's
Day, there were 225 lbs. of a mixture of white and red M&M's found
in a store room. This mixture sold for $.55 per pound. The company
wants to add blue M&M's for a new mixture for the 4th of July. How
many pounds of blue M&M's (at $.85 per pound) should they add to
the red/white mixture if they'd like to sell it for $.65 per pound?
Halloween and
Thanksgiving are right around the corner. The marketing team wants
to develop 10,000 pounds of a special mixture of M&M's that will
rival the sale of candy corn. They plan to develop a batch of yellow/orange
M&M's with some brown M&M's and sell it at $.53 per pound (since
candy corn sells for $.55 per pound). The yellow/orange mixture
sells for $.65 per pound and brown M&M's sell for $.25 per pound.
How much of each should they put in this special holiday mixture? YOUR TURN with real data...
Count the M&M Mini's in your box and record them in the table below...
-
| Color |
Brown |
Green |
Orange |
Blue |
Red |
Pink |
Yellow |
Total Number |
| number
of each color |
. |
. |
. |
. |
. |
. |
. |
. |
The M&M Mini's
have begun to take the world by storm since the red and yellow M&M's
let them out. The addition of pink has made it very popular. Using
your box of mini's, fill out the information below....
# of pink M&M's = ________________
total # of M&M's = ___________________
What percent of the M&M's in your box is pink? ______________________
-
If you
were to make a box of M&M's that was 55% pink, how many pink
M&M's would you need to add to the M&M's in your box?
- What if
the new box was to be 75% pink, how many pinks would you have
to add?
If the percentages
of colors in your box is correct for an entire batch of M&M's, what
is the percent of M&M's that are
-
-
red
in a mixture of red and orange?
-
red
in a mixture of red and pink?
-
red
in a mixture of green and blue?
If you took
60 pounds of your red/orange group and added it to the 75 pounds
of the extra red/pink group, what would the percent of red be
in the new group? Now, back to more problems....
If a mixture
of yellow/orange M&M's cost $ .65 a pound and a mixture of blue/green
M&M's cost $ .78 per pound, how much of each would it take to make
a mixture that sells for $ .73 per pound if you want a total of
500 pounds?
The Marketing
Department had workers make mixtures of yellow, pink, and green
for Spring, but forgot to tell them to use the leftover mixture
of green and white from St. Patrick's Day. The Spring mixture (yellow,
pink, and green) is 20% green. The St. Patrick's Day mixture is
65 % green. The final mixture for Spring is to be 30% green. How
much of the yellow/pink/green mixture should be added to the 10,500
pounds of leftover St. Patrick's Day mixture.
The dye makers
are in a bunch of trouble. Instead of making 45 quarts of brown
dye that is 30% yellow, they misread the directions and made it
80% yellow. The company won't have this and they don't have enough
dye to throw this batch out. They have to FIX it! They need to add
more of the red/blue mixture to their "mistake batch." How much
should they add to make the new mixture 30% yellow?
The M&M Corporation
has been so successful that they need to invest $600,000 in profits.
They currently have two bankers on their board of directors and
so they must invest some of the money in each of the two banks.
Bank A offers an annual interest rate of 4.5% and Bank B offers
a 6% interest rate. At the end of the year, the company needs to
make $27,900 in interest. How much should they invest in each account
to earn this amount of money? Would you recommend that they reconsider
their target amount of interest to earn? Why or why not? Now try these....
There is talk
of a new product - M&M mini ice cream. If one gallon of ice cream
had 9.2% M&M's, how much ice cream containing 2% M&M's should be
added to the ice cream to obtain ice cream that is 6.5% M&M's?
My family is
going on vacation to the M&M Studios this summer. The total cost
of the tickets is $92.50 for 2 adults and 3 children. An adult ticket
costs $5 more than a child's ticket. Find the cost of each ticket.
The Blue M&M
spent $5.61 on stamps to mail his poetry to his publisher. He bought
the same number of 2- and 5-cent stamps and twice that number of
22-cent stamps. How many of each type of stamp did he buy?
An advertisement
for M&M's claims that there are 10% of each of the blue, green,
and orange M&M's, 20% of each of the yellow and red M&M's, and 30%
brown.
-
-
Therefore,
in a bag of 345 M&M's, how many of each color should I find
in the bag? Assuming that the M&M people did a good job with
quality control, there cannot be any broken M&M's in your bag!
-
If your
box of mini's did not contain any pink M&M's how many of each
color should I have found in your box assuming that the number
of mini's in your box remained the same?
-
You've
just been hired by the Mars Candy Company in the M&M division.
They've just announced that there will be 15 colors of M&M's
coming soon!
-
Name
the colors that you will suggest for the 15 and propose
the % of each to manufacture in each batch. Remember that
your percents must total 100 %!
-
Then,
propose two new color combinations of 3 or more colors and
the percentage of each color in each of these combinations.
-
Finally,
use this information to write and solve two mixture problems
for the M&M Candy Co.
</0l>
Internet
Sites with more mixture problems include:
Resource
in Print
"Tug of War," by William D. Telford, Jr. Mathematics Teacher,
February, 1993 by the National Council of Teachers of Mathematics
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