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Mathematical Word Problems
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Mathematical Word Problems
• The key to word problems is to read
the question thoroughly and slowly.
Don’t be overwhelmed. Just break it
down and write it out step by step. If
necessary, draw diagrams to help
you understand the scenario.
Mathematical Word Problems
• Take each sentence individually
and investigate the information it
gives you. Think of yourself as a
Crime Scene Investigator (CSI),
solve the mystery, and watch the
answer unfold before your eyes….
Mathematical Word Problems
• Number One
• Problem: Brienne owns four cars.
Gavan owns twice as many cars as
Brienne. Ashley owns one less car
than Gavan. Ashley is buying four
new tires for every car she owns.
Each tire costs one hundred dollars.
How much money will the tires cost
altogether?
Mathematical Word Problems
• Solution: We need to break this down and
dissect the information in each sentence.
• First… Brienne owns four cars… So Brienne
owns 4 cars.
• Second… Gavan owns twice as many cars as
Brienne…. So…2 x 4 = 8 cars for Gavan.
• Next…. Ashley owns one less car than
Gavan…. So…8 – 1 = 7 cars for Ashley.
• Now…. Ashley is buying four new tires for every
car she owns… So… 4 x 7 = 28 tires
• Last…Each tire costs one hundred
dollars….So… $100 x 28 = $2800 for her new
tires.
Mathematical Word Problems
• Number Two
• Problem: Anthony and Carolyn have bug
collections. If they combined their collections,
they would have a collection of twenty bugs.
Which of the following statements could not be
true?
• a. Carolyn has a dozen bugs.
b. Anthony has eleven bugs.
c. Anthony has one more bug than Carolyn.
d. Carolyn has two more bugs than Anthony.
e. Carolyn has one bug.
Mathematical Word Problems
• Solution: Again, each sentence in the
multiple choice needs to be dissected to
find the one that is false. The key is that
the total bugs are 20.
• Can Carolyn have a dozen bugs? If she
has 12, then Anthony has 8 because 2012=8
• This could be true.
• Can Anthony have eleven bugs? If he
has 11, then Carolyn has 9 because 2011=9
• This could be true also.
Mathematical Word Problems
• Can Anthony have one more bug than Carolyn?
This one takes some thought. But if you use the
two examples above, you can easily decipher
this one. If Anthony has 11 bugs for instance,
can Carolyn have 10? No because that would =
21 bugs between them. Well, can Anthony have
10 and Carolyn have 9 bugs? No because that
would =19 bugs between them. Notice that one
cannot have an even number and the other an
odd number of bugs. The total 20 is an even
number. This indicates that both will have even
numbers of bugs or both will have odd numbers
of bugs. (Note the first two possible answers.)
Mathematical Word Problems
• This is obviously your FALSE statement, but
with all word problems it is wise to read the rest
of the options just in case there it more than
one answer. This also solidifies your confidence
in your answer or can help you recognize a
mistake in your calculations.
• Can Carolyn have two more bugs than
Anthony? True. This is demonstrated above in
the second possible answer where Anthony has
11 and Carolyn has 9.
• Can Carolyn have one bug? True. Anthony
could easily have 19 of the bugs.
Mathematical Word Problems
• Number Three
• Problem: There were 24 apples
given out to the children at Faith’s
Halloween party. Each child got
three apples. How many children
were at the party?
Mathematical Word Problems
• Solution: Once again, pay attention to
all the information given.
• We have 24 apples.
• Each child got 3 apples.
• There are more apples than children if
each got 3 apples.
• So we divide 24 apples by 3 apples and
we get 8 children.
• 24 / 3 = 8 or another way to look at it is:
? x 3 = 24 The answer is still 8.
Mathematical Word Problems
• Number Four
• Problem: How many ghosts are in
the haunted house? Here are some
clues: There are more than the
number of days in October. There
are less than the product of 7 and
5. The answer is an odd number.
Mathematical Word Problems
• Solution: October has 31 days, so
the number is > 31.
• We are also told that the number is
less than the product of 7 and 5.
•
Hint: Product = multiplication
•
Sum = addition
•
Difference = subtraction
Mathematical Word Problems
• Ratio = division
• However, even not knowing the word
product means multiply, we know that if
we add 7+5 we get 12 and the number
can’t be less than 12 and greater than 31
at the same time. But if we multiply, we
get 7 x 5 = 35. So the number is < 35.
• Now the answer comes easily….which
number is > 31 and < 35 and an odd #?
• 31, 32, 33, 34, 35
Mathematical Word Problems
• Number Five
• Problem: Sandra is playing in a
tennis doubles tournament. The
rules say that the average age of
the pair of players on each side
must be ten years old or younger.
Sandra is eight years old. Her
partner must be _____ years old or
younger.
Mathematical Word Problems
• Solution: Here the average age must be 10
years old.
• This means that if there are 2 players and if we
add their ages together and divide by 2 it has to
be at least 10!
• So the least their combined age could be would
be 20 because… 20 / 2 = 10
• If their combined ages totaled 24, then 24 / 2 =
12 and they still meet the minimum age
requirements.
• However if their combined age was 18, then 18
/ 2 = 9 and this is less than the minimum age
requirement.
Mathematical Word Problems
• So Sandra and her partner together
must = 20. If Sandra is 8, then her
partner must be 20 – 8 = 12 years old.
• Does this work? Let’s check our work:
• 8 yrs old + 12 yrs old = 20 years old….
Divide by 2 for the average age of 10!
• Good luck in the tournament girls….
• And now good luck to you as you take
the exam for this module!
Mathematical Word Problems
You must make a perfect score of 100% to pass.
Click here to take the test for this module.