Transcript Answer

What are the challenges?
• To know how to translate word problems
into a workable mathematical equation.
• To know where to start and how to go
about figuring out the answer.
• To know the strategies needed to break
down a word problem so it is clear and
easy to solve.
6 Steps
for
Solving
Math Word Problems
Step 1
Convert the words into an equation.
•Read through the entire problem first.
•Don’t try to solve it when you’ve only read one sentence.
•Read the problem completely in order to get the whole
picture.
•Effectively translate and solve the problem.
Step 2
Go back to the beginning.
•Reread the first sentence.
•Write down what you know and what you don’t know.
•Use variables to stand for the unknowns and clearly label
what they stand for.
•Do the same for the second sentence and each following
sentence.
Step 3
Look for Signal Words that mean
certain mathematical
operations.
Signal Words
Addition
Subtraction
Multiplication
Division
Equals
Step 4
Perform the required
operations.
Step 5
Make sure you are answering the
question that is being asked of you.
•One step may seem like it’s the answer, but it may
take several steps to arrive at the final answer.
•Don’t lose sight of what the word problem is asking for or
asking you to do.
•Label the answer with the unit of measurement or with
the object the question is requesting.
Step 6
Mentally or on paper check your answer to
make sure it is correct and makes sense.
•Replace the variable in each step with your answer.
•Calculate the equation with the now known variable to see if
it satisfies the equation.
If it does, then you’re done!
Practice, Practice, Practice!
Mastering word
problems requires
practice!
Understanding Algebra Word
Problems
*Represent a given situation using algebraic
expressions or equations in one variable.
*Simplify and evaluate algebraic expressions.
The biggest challenge to solving word problems is
figuring out whether to add, subtract, multiply or divide.
Words Meaning
Addition
Words Meaning
Subtraction
Words Meaning Words Meaning
Multiplication
Division
and
increased
more
more than
plus
sum
total
decreased
difference
less
less than
left
lower than
minus
double
half (× ½)
product
times
triple
twice
divide into
half (÷ 2)
divide by
divide among
quotient
To solve a word problem, you must first interpret
the action you need to perform and then choose
the correct operation for that action.
Action
Operation
Possible Question Clues
Combine
Add
How many all together?
Combine equal groups
Multiply
How many all together?
Separate
Subtract
How many more? How many less?
Separate into equal groups
Divide
How many equal groups?
Word Phrases
+
–
• a number plus 5
• add 5 to a number
• sum of a number and 5
• 5 more than a number
• a number increased by 5
• a number minus 11
• subtract 11 from a number
• difference of a number and 11
• 11 less than a number
• a number decreased by 11
Expression
n+5
x  11

• 3 times a number
• 3 multiplied by a number
• product of 3 and a number
3m

• a number divided by 7
• 7 divided into a number
• quotient of a number and 7
a
or a  7
7
Word Problems
Solve the word problem:
A number increased by 14 is
49.
Answer:
n + 14 = 49
n = 35
Solve the word problem: Find the number
Twenty-nine more than a number is
52.
Answer:
n + 29 = 52
n = 23
Solve the word problem: Find the number
One-half of a number is 9.
Answer:
½(n)= 9
n = 18
Solve the word problem: Find the number
The sum of a number and 79 is 143.
Answer:
n + 79 = 143
n = 64
Solve the word problem: Find the number
A number decreased by 28 is 76.
Answer:
n - 28 = 76
n = 104
Solve the word problem:
Lisa is cooking muffins. The recipe
calls for 7 cups of sugar. She has
already put in 2 cups. How many
more cups does she need to put in?
Answer:
2+c=7
c=5
Solve the word problem:
How many packages of diapers can
you buy with $40 if one package cost
$8?
Answer:
p(8) = 40
p=5
Word Problems
Multiple step
Solve the word problem:
331 students went on a field trip. Six
buses were filled and 7 students
traveled in cars. How many students
were in each bus?
(assume each bus was equally filled)
Answer:
6b + 7 = 331
b = 54
Solve the word problem:
Carter had $24 to spend on seven
pencils. After buying them he had $10.
How much did each pencil cost?
Answer:
7p + 10 = 24
or
24 – 7p = 10
p = $2
Solve the word problem:
The sum of three consecutive numbers
is 72. What is the smallest of these
numbers?
Answer:
x + (x+1) + (x+2) = 72
x = 23
Solve the word problem:
The sum of three consecutive even
numbers is 48. What is the smallest of
these numbers?
Answer:
x + (x+2) + (x+4) = 48
x = 14
Solve the word problem:
You bought a magazine for $5 and four
erasers. You spent a total of $25. How
much did each eraser cost?
Answer:
5 + 4e = 25
e = $5
Solve the word problem:
The Math Team made some pies to sell at a
basketball game to raise money for the new
math books. The cafeteria contributed four
pies to the sale. Each pie was then cut into
five pieces and sold. There were a total of
60 pieces to sell. How many pies did the
Math Team make?
Answer:
5(p+4)= 60
p=8
Solve the word problem:
When the magic number is increased
by 32 and this result is tripled, the final
result is 246. What is the magic
number?
Answer:
3(n + 32) = 246
n = 50
Solve the word problem:
On a 30-question test, Makenzie
earns 5 points for each correct
answer and loses 3 points for every
incorrect answer. If she answers
all the questions, and her score
was 6, how many did she answer
correctly?
Answer:
5c – 3(30 – c) = 6
c = 12
The ratio of kids to adults is 5 to 2.
If there is 14 adults, how many kids
are there?
Kids:adults=5:2
adults=14
Or lets try…
Find the factor:
5x kids
2x adults
2x = 14
x = 7 (factor)
Therefore: 5x (kids)
5·7 =35
Answer: 35 kids
The ratio of kids to adults is 3 to
5. If there are 26 more adults
than kids, how many kids are
there?
Kids:adults=3:5
Find the factor:
3x kids & 5x adults
adults – kids=26
5x-3x=26
2x=26
x = 13 (factor)
Therefore: 3x (kids)
3·13 =39
Answer: 39 kids
30 boys and girls are planning
for a picnic. There are a ratio of
3 girls to 7 boys. How many
boys are there?
Answer:
3x + 7x = 30
10x = 30
x=3
3·3
3·7
9/21 (girls/boys)
I have 70 friends. Among them
are 11 girls for every 3 boys.
How many friends are boys?
How many are girls?
Answer:
find the factor
11x + 3x = 70
14x=70
x=5 (factor)
11·5=55 girls
3·5=15 boys
The ratio of dogs to cats is 9 to
2. If there are 72 dogs, how
many total dogs and cats are
there?
Answer:
88
To get a shade of orange paint,
we mix white, red, & yellow in
the ratio 2:5:4. If we need 6
gallons of orange paint, then
how many gallons of each color
do we need?
Answer:
White=2x, red=5x, yellow=4x
2x+5x+4x=6
X=6/11
White=12/11, red=30/11,
yellow=24/11
The top 3 cash prizes in the
math tournament are in the
ratio 5:2:1. The 1st place prize
rd
is $20,000 more than the 3
place prize. How much is the
second place prize?
Answer:
1st=5x, 2nd=2x, 3rd=1x
5x-1x=20000
X=5000
nd
2
place = 2x=2∙5000=$10,000
Lauren divided her money in
the ratio 4:2 between Haley and
Makenzie. Haley got the
smaller amount of $1256. How
much did Makenzie receive?
4/2 = M/1256
2M = 4·1256
M =2512
12 miles is approximately equal
to 6 km. How many miles are
equal to 42 km?
Answer:
x⁄
42
¹²⁄₆ =
¹²⁄₆ · 42 = 84
12 miles is approximately equal
to 6 km. How many km are
equal to 18 miles?
Answer:
9
Direct Variation
if y varies directly as x and y = 10
as x = 2.4, find x when y =15
10 15

2.4
x
Direct Variation
If y varies directly with x and y =
12 when x = 2, find y when x = 8.
12 y

2 8
Inverse Variation
If y varies inversely with x and
y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y=3
Inverse Variation
If y varies inversely as x and x = 18
when y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 13.5
How much tax will
Carter pay on a
surround-sound
system that cost
$1885.00 if the tax is
5%
Answer:
Equation: n = 0.05 ∙ 1885
n = $94.25
Bob now earns $9.50
per hour. This is
125% of what she
earned last year.
What did she earn
per hour last year?
Answer:
Equation: 9.5 = n ∙ 1.25
n = $7.60
I paid $8400 in federal
and state income taxes
last year, which amounted
to 28% of my annual
income. What was my
income last year?
Answer:
Equation: 8400 = 0.28 ∙ n
n = $30,000
Competition
Scoring:
5 points – 1st Interval (0-30 seconds)
3 points – 2nd Interval (30-60 seconds)
1 points – 3rd Interval (60-90 seconds)
Ready…?
What is the quotient of 3.5316
divided by 3.27?
Answer:
1.08
Every large pack of gum has 8
pieces and every small pack of gum
has 3 pieces. Mary has 7 small
packs and 4 large packs. How many
pieces of gum does Mary have
altogether?
Answer:
53
Jason has 17 pencils and Shannon
has 43 pencils. How many pencils
must Shannon give Jason in order
for them to have the same number
of pencils?
Answer:
13
Ravi's age is double Ranu's age.
The product of their ages in years
is 72. How old is Ranu?
Answer:
6
Billy brought a large box of chocolates to
school. In his first class, he gave half of the
chocolates in the box to his teacher. In his
second class, he gave half of his remaining
chocolates to his best friend. At lunch, he
ate half of his remaining chocolates. If he
had 3 pieces of chocolate left at the end of
lunch, then how many pieces were in the
box when Billy arrived at school?
Answer:
24
Your brother traveled 117 miles in
2.25 hours to come home for school
break. What’s the average speed
that he was traveling?
Answer:
52 mph
What is thirty-four hundredths
minus fifty-two thousandths?
Answer:
0.288
You have 15 yards of ribbon for your
gift boxes. Each box gets the same
amount of ribbon. How much
ribbon will each of your 20 gift
boxes get?
Answer:
0.75 yards
What is two and three thousandths
times twenty-one hundredths?
Answer:
0.4206
Sam gave Jen 1/2 of his jujubes. Jen
ate 1/2 of the jujubes and gave the
rest to Kyle. Kyle kept 8 of the jujubes
and gave the last 10 to Kim. How many
jujubes did Jen eat?
Answer:
18
You finally get an allowance! You
put $2 away in January, $4 away in
February, $8 away in March, $16
away in April and followed this
savings pattern through to
December. How much money do
you have in 12 months?
Answer:
$4096.00
Jeff has 1/2 pizza left in the fridge. At
breakfast he at 1/3 of it. What fraction of
the original pizza does he have left for
lunch?
Answer:
1/3
What is one-sixth of 678?
Answer:
113
I’m thinking of two number, 12 and
another number. 12 and my other
number have a greatest common
factor of 6 and their least common
multiple is 36. What’s the other
number I’m thinking of?
Answer:
18
Tom had a platter of chocolate wafers.
He ate 5 of them and then gave his
brother 3, he then handed them to his
ball team of 8 members. The first
player to arrive took 1, the second
player took 3, the third player took 5
and so on. When the last player took
his, the platter was empty. How many
chocolate wafers did Tom start with?
Answer:
72
Jasmine has 50 marbles
in a bag. 20% of the
marbles are blue. How
many marbles are blue?
Answer:
10
An Olympic runner set a record for the
100m dash. The time was ten and
sixty-two hundredths seconds. How
would you write this as a number?
Answer:
10.62
The tables at the party are shaped like
the hexagon. If you put the tables
together, how many would you need
for 50 people?
Answer:
12
At your birthday party, you had 7 8slice
pizzas. 41 slices were eaten. What
fraction of pizza is left?
Answer:
1
7/
8
Peter uses quick fix glue to hold a
bamboo rod. One piece of the rod
measures 1 ⅕ meters and another
piece measures 2 ⅔ meters. What is
the total length of bamboo rod after it
has been glued together?
Answer:
3
13/
meters
15
What is the reciprocal of
eight and one-third?
Answer:
3/25
Which property states:
(5)(17)(23) = (5)(23)(17)
Answer:
Commutative
Property of
multiplication
Find the product of three and fortyeight thousandths with four and six
hundredths.
(round your answer to the nearest hundredth)
Answer:
12.37
A triangle has one angle that is 62
degrees and one angle that has a
measure of 41 degrees. What is
the measure of the third angle?
Answer:
77
What is the sum of the
GCF of 17 and 51 and the
first seven prime
numbers?
Answer:
75
Write the reciprocal of 2⅛
Answer:
8/17
What is 75.5% of 60?
Answer:
45.3
What is the base of a
triangle with a height of 4
cm and an area of 28 cm²?
Answer:
14
A student had the following
scores in math: 89, 97, 100, 85,
93, 73, and 100. What is the
positive difference
in the median and mode?
Answer:
7
What is the 7th number in
the following sequence?
1, 3, 9, 27, 81, __, __
Answer:
729
What is the measure of the
complement of a 60° angle?
Answer:
30°
If a + 6 = 12 and 7b = 49, what is
the value of 3ab?
Answer:
126
What is the product of all the
positive odd number factors of
50?
Answer:
125
What is the area of a square
with perimeter of 48 cm?
Answer:
144
2
cm
What is 25% of 60% of 180?
Answer:
27
Find the sum of the first 10
positive integers that are not
prime.
Answer:
95
a b = 5b – a, then what does
-7 -4 equal?
Answer:
-13
What is the smallest number
divisible by 8, 12, and 20?
Answer:
120
Of the numbers
2, 15, 19, 41, 55, 87 and 91,
what is the sum of the
composite numbers?
Answer:
248
Find the total cost of a camera
marked 30% off the original
price of $59.99,
plus a 7% sales tax.
Answer:
$44.93
What is the mean for the given
data:
36, 25, 28, 39, and 30.
Answer:
31.6
The scale of a map is 1 in. = 20 mi.
Find the actual distance, in miles,
represented by 2 ¾ inches on the
map?
Answer:
55
A right triangle has side
measurements of 8 in., 15 in., and
17 in. What is the area of this
triangle?
Answer:
60
In the equation 2x + y = 8, find the
value of x when y = -16.
Answer:
12
Using the diagram below, how
many students studied exactly two
days for a test?
Mon.
3
Tues.
6
5
4
1
2
3
Wed.
Answer:
6
A rectangular room measures 19 ft.
by 18 ft. How many square yards
of tile are required to cover the
floor?
Answer:
38
Mary spent $21 on a taxi ride,
$43.30 on a concert ticket, and
$32.50 on food. If she started with
$130.00 , how much is left?
Answer:
$33.20
Tom spent $4.25 to wash his car.
If one quarter operates the car wash
for 60 seconds, how many minutes
did he was his car?
Answer:
17
Two angles of a triangle
measure 50° and 33°.
Find the measure of the third
angle.
Answer:
97°
Ford makes 7 red cars for every
4 white cars made. If it makes
16 white cars a day, how many
red cars will it make a day?
Answer:
28
John has twice as many dimes
as nickels. If the value of the
dimes is $5.00, find the value of
the nickels.
Answer:
$1.25
Two dozen pencils are in a bag.
5 are blue, 3 are red, and the
rest are yellow. What is the
probability of drawing a yellow
pencil?
Answer:
2/3
What is 60% of 75?
Answer:
45
Find the sum of the next two
numbers in the following
sequence:
1, 8, 27, 64, …
Answer:
341
Six times a number is eight
more then twice the number.
What is the number?
Answer:
2
How many of the following
numbers are perfect squares?
1, 2, 4, 6, 9, 15, 16, 27, 32,
36, 48, 50, 64, 89
Answer:
6