Date post: | 17-Nov-2014 |
Category: |
Education |
Upload: | don-simmons |
View: | 2,609 times |
Download: | 2 times |
Algebra 2
WORD PROBLEM WARM-UP 1
How long will it take 100 storks to catch 100 frogs,
when five storks need five minutes to catch five
frogs?
Answer: 5 minutes.
WARM-UP 1
Algebra 2
WORD PROBLEM WARM-UP 1
Logan, Vikrant and Emily differ greatly in height.
Vikrant is 14” taller than Emily. The difference
between Vikrant and Logan is two inches less than
between Logan and Emily. Vikrant at 6’-6” is the
tallest of the three. How tall are Logan and Emily?
Answer: If Vikrant is 6’-6”, then Emily must be 5’-
4”, and Logan must be 6’-0” (8” greater than Emily
and 6” less than Vikrant).
WARM-UP 2
Algebra 2
WORD PROBLEM WARM-UP 1
Find the numbers that will replace letters a and b so that the five-digit number will be divisible by 36:
19a 9b
(Note: There are two possible solutions)
Answer: 19692 and 19296. To be divisible by 36, a number must be divisible by 9 and 4. To be divisible by 9, the sum of the digits must be divisible by 9. The last two digits must be divisible by 4. Therefore, b can be either 2 or 6.
WARM-UP 3
Algebra 2
WORD PROBLEM WARM-UP 1
On the way home from school, Tom found out that
he got only half the allowance that Mark got. Suzi is
three years older and receives three times what
Tom gets. Together, the three receive $144. How
much is each student getting?
Answer: Divide the total by 6: 144/6 =24. Therefore
Tom gets $24; Mark gets $48; and Suzi receives
$72.
WARM-UP 4
Algebra 2
WORD PROBLEM WARM-UP 1
Students in class with less than 30 students finished
their algebra test. 1/3 of the class received a “B”, ¼
received a “B-”, and 1/6 received a “C”. 1/8 of the
class failed. How many students received an “A”.
Answer: There were 3 “A’s”. Look for a common
denominator – the only one smaller than 30 is 24.
When you add up the known fractions, you have
21/24.
WARM-UP 5
Algebra 2
WORD PROBLEM WARM-UP 1
On a road 75 miles long, two trucks approach each
other. Truck A is traveling at 55 mph while Truck B is
traveling at 80 mph. What is the distance between
the two trucks one minute before they collide?
Answer: 2.25 miles. The trucks are approaching
each other at a speed of 135 mph (55 + 80).
135/60=2.25
WARM-UP 6
Algebra 2
WORD PROBLEM WARM-UP 1
Ten years more than three times Charlie’s age is
two years less than five times his age. How old is
he?
Answer: 6 years.
WARM-UP 7
Algebra 2
WORD PROBLEM WARM-UP 1
The average age of the three Wilson children is 7
years. If the two younger children are 4 years old
and 7 years old, how many years old is the oldest
child?
Answer: 10 years.
WARM-UP 8
Algebra 2
WORD PROBLEM WARM-UP 1
A box of 100 personalized pencils costs $30. How
many dollars does it cost to buy 2500 pencils?
Answer: $750.
WARM-UP 9
Algebra 2
WORD PROBLEM WARM-UP 1
Jeff has an equal number of nickels, dimes and
quarters worth a total of $1.20. Anne has one
more of each type of coin than Jeff has. How
many coins does Anne have?
Answer: 12 coins.
WARM-UP 10
If x y = 6 and x + y = 12, what is the value of y?
Algebra 2
WORD PROBLEM WARM-UP 1
Alex has fifteen nickels and dimes. He has seven
more nickels than dimes. How many of each coin
does he have?
Answer: 11 nickels and 4 dimes.
WARM-UP 11
If x y = 6 and x + y = 12, what is the value of y?
15
7
( 7) 15
2 7 15
4
n d
n d
d d
d
d
Algebra 2
WORD PROBLEM WARM-UP 1
Joel has two fewer quarters than dimes and a total
of fourteen dimes and quarters. How many of each
coin does he have?
Answer: 8 dimes and 6 quarters.
WARM-UP 12
If x y = 6 and x + y = 12, what is the value of y?
2
14
( 2) 14
2 2 14
8
q d
q d
d d
d
d
Algebra 2
WORD PROBLEM WARM-UP 1
Ten years more than three times Charlie’s age is
two years less than five times his age. How old is
Charlie?
Answer: 6 years old.
WARM-UP 13
If x y = 6 and x + y = 12, what is the value of y?
3 10 5 2C C
Algebra 2
WORD PROBLEM WARM-UP 1
When Alice is three times as old as she was five
years ago, she will be twice her present age. How
old is she?
Answer: 15 years old.
WARM-UP 14
If x y = 6 and x + y = 12, what is the value of y?
3( 5) 2A A
Algebra 2
WORD PROBLEM WARM-UP 1
The sum of Gary’s and Vivian’s ages is twenty-three
years. Gary is seven years older than Vivian. How
old is each person?
Answer: Vivian – 8 years; Gary - 15 years.
WARM-UP 15
23
7
( 7) 23
2 7 23
G V
G V
V V
V
Algebra 2
WORD PROBLEM WARM-UP 1
Brad is five years younger than Louise. The sum of
their ages is thirty-one years. How old is each
person?
Answer: Brad – 13 years; Louise – 18 years.
WARM-UP 16
5
31
( 5) 31
2 5 31
B L
B L
L L
L
Algebra 2
WORD PROBLEM WARM-UP 1
The sum of the ages of Juan and Herman is twenty-
four years. Juan is twice as old as Herman. How old
is each?
Answer: Juan – 16 years; Herman – 8 years.
WARM-UP 17
24
2
(2 ) 24
3 24
J H
J H
H H
H
Algebra 2
WORD PROBLEM WARM-UP 1
If Edith were five years older, she would be twice
Fred’s age. If she were three years younger, she
would be exactly his age. How old is each one?
Answer: Edith – 11 years; Fred – 8 years.
WARM-UP 18
5 2
3
5 2( 3)
5 2 6
E F
E F
E E
E E
Algebra 2
WORD PROBLEM WARM-UP 1
When Leonard is five years older than double his
present age, he will be three times as old as he was
a year ago. How old is he?
Answer: Leonard – 8 years.
WARM-UP 19
2 5 3( 1)
2 5 3 3
8
L L
L L
L
Algebra 2
WORD PROBLEM WARM-UP 1
If Karen were two years older than she is, she would
be twice as old as Larry, who is eight years younger
than she. How old is each?
Answer: Karen – 18 years; Larry – 10 years.
WARM-UP 20
2 5 3( 1)
2 5 3 3
L L
L L
Algebra 2
WORD PROBLEM WARM-UP 1
Yolanda has a total of thirty-seven nickels and
dimes. The dimes come to 40¢ more than the
nickels. How many of each coin does she have?
Answer: 22 nickels; 15 dimes.
WARM-UP 21
37
10 5 40
4 372
n d
d n
nn
Algebra 2
WORD PROBLEM WARM-UP 1
Sue has a total of forty nickels and dimes. She has
two more dimes than nickels. If she had eleven
more coins, she would have 90¢ more. How many
nickels and dimes does she have?
Answer: 19 nickels; 21 dimes.
WARM-UP 22
40
2
( 2) 40
n d
d n
n n
Algebra 2
WORD PROBLEM WARM-UP 1
Lisa has a total of fifty-four nickels and dimes. If she
had three more nickels, the value of the coins would
be $4. How many of each does she have?
Answer: 31 nickels; 23 dimes.
WARM-UP 23
54
5( 3) 10 400 or
5 10 400 15
n d
n d
n d
Algebra 2
WORD PROBLEM WARM-UP 1
Amy has two more nickels than dimes and five more
dimes than quarters. Her nickels, dimes, and
quarters total $3.25. How many of each kind does
she have?
Answer: 13 nickels; 11 dimes; 6 quarters.
WARM-UP 24
2
5
5 10 25 325
n d
d q
n d q
Algebra 2
WORD PROBLEM WARM-UP 1
Luke has three times as many nickels as dimes and
five times as many pennies as nickels. He has
$2.80. How many of each coin does he have?
Answer: 105 pennies; 21 nickels; 7 dimes.
WARM-UP 25
3
5
5 10 280
n d
p n
p n d
Algebra 2
WORD PROBLEM WARM-UP 1
If Eustace had twice as many nickels and half as
many quarters, he would have 60¢ less. Suppose he
now has sixteen nickels and quarters. How many of
each kind does he have?
Answer: 105 pennies; 21 nickels; 7 dimes.
WARM-UP 26
3
5
5 10 280
n d
p n
p n d
Algebra 2
WORD PROBLEM WARM-UP 1
A rectangle whose perimeter is fifty feet is five feet
longer than it is wide. What are its dimensions?
What is its area?
Answer: w = 10 ft; l = 15 ft; A = 150 square feet
WARM-UP 27
2 2
2 2( 5)
4 10
P w l
P w w
P w
Algebra 2
WORD PROBLEM WARM-UP 1
You are given the formula A = bc.
Rewrite the given equation to show the effect of
each statement. If b is increased by 6 and c is…
a. decreased by 2, then A increases by 15.b. increased by 2, then A doubles.
Answer:
WARM-UP 28
a. 15 ( 6)( 2)
b. 2 ( 6)( 2)
A b c
A b c
Algebra 2
WORD PROBLEM WARM-UP 1
You are given the formula A = bc.
What is the effect on A if…
a. b is doubled and c is unchanged?b. b is doubled and c is halved?c. b is tripled and c is doubled?
Answer: a. A is doubled
b. A is unchanged
c. A is six times as much
WARM-UP 29
Algebra 2
WORD PROBLEM WARM-UP 1
You are given the formula for the area of a
rectangle,
A = lw, where l and w are in feet. Rewrite the given
equation to show the effect of each statement.
a. If the length increases by 5 feet and the width is unchanged, then the area increases by 40 square feet.
b. The width is two-thirds of the length.
Answer:
WARM-UP 30
2
a. 40 ( 5)
2b.
3
A l w
A l
Algebra 2
WORD PROBLEM WARM-UP 1
75% of the length of a rectangle and 20% of its
width are eliminated. How does the area of the
resulting rectangle compare with the area of the
original rectangle?
Answer: New area is 20% of original area
WARM-UP 31
(.25 )(.80 ) .2( ) .20
A lw
l w lw A
Algebra 2
WORD PROBLEM WARM-UP 1
The width of a rectangle is 40 cm less than its
perimeter. The rectangle’s area is 102 sq. cm. What
are the rectangle’s dimensions?
Answer: 6 cm by 17 cm
WARM-UP 32
2( )
40
102
P l w
w P
lw
Algebra 2
WORD PROBLEM WARM-UP 1
A rectangle is three centimeters longer than it is
wide. If its length were to be decreased by two
centimeters, its area would decrease by thirty
square centimeters. What is its area?
Answer: 270 square centimeters
WARM-UP 33
3
30 ( 2)
l w
A lw
A l w
Algebra 2
WORD PROBLEM WARM-UP 1
Porter drove for 3 hours at 40 mph and for 2 hours
at 50 mph. What was her average speed during that
time?
Answer: 44 mph
WARM-UP 34
1 2
sumof distancesaveragespeed=
sumof times
40(3); 50(2)
D rt
D D
Algebra 2
WORD PROBLEM WARM-UP 1
A car traveled from A to B at 50 mph, from B to C at
60 mph, and returned (C to B to A) at 80 mph. What
was the average speed on the round trip if the
distance from A to B is 100 miles and from B to C is
120 miles?
Answer:
WARM-UP 35
1 2 1 2
1 2 1 2 3
565 mph
27sumof distances
averagespeed=sumof times
2( );
a
D D D Da a
t t t t t
Algebra 2
WORD PROBLEM WARM-UP 1
It took 3 hours and 40 minutes for a car traveling at
60 mph to go from A to B.
a) How long will the return trip take if the car
travels at 80 mph?
b) What must the car’s average speed be from B to
A if the return trip is to be made in 2-1/2 hours?
Answer: 2.75 hours D = 60 x 3-2/3 = 220
miles
220/80 = 2.75
hours
WARM-UP 36
Algebra 2
WORD PROBLEM WARM-UP 1
A road runs parallel to a railroad track. A car
traveling an average speed of 50 mph starts out on
the road at noon. One hour later, a train traveling
an average speed of 90 mph in the same direction
as the car passes the spot where the car started. If
the car and the train continue to travel along
parallel paths, at what time will the train overtake
the car?
Answer: 2:15 pm. D = 50t = 90(t-1)
WARM-UP 37
Algebra 2
WORD PROBLEM WARM-UP 1
A car traveling parallel to a railroad track at an
average speed of 55 mph starts out on the road at
noon. A train traveling at an average speed of 95
mph in the same direction also starts at noon. They
both arrive at the same spot at 2:15 pm. How far
ahead of the train was the car when they both
began?
90 miles. Dt= 95(9/4); Dc=55(9/4)
Difference = Dt- Dc
WARM-UP 38
Algebra 2
WORD PROBLEM WARM-UP 1
Two planes fly at the same speed in still air. They
leave the airport at the same time and fly in the
same air current but in opposite directions. The
plane going with the air current is 1,470 miles from
the airport 3 hours after takeoff. The plane flying
against the air current is 2,050 miles from the
airport 5 hours after takeoff. What is the speed of
the air current?
40 mph. 1470 = (r + c)(3); 2050 = (r – c)(5)
WARM-UP 39
Algebra 2
WORD PROBLEM WARM-UP 1
Two canoeists paddle the same rate in still water.
One canoeist paddled upstream for 1-1/2 hours and
was 18 miles from the starting point. The other
canoeist paddled downstream for 2 hours and was
36 miles from the starting point. At what speed do
the canoeists paddle in still water?
15 mph. 18 = (r – c)(1.5); 36 = (r + c)(2)
WARM-UP 40
Algebra 2
WORD PROBLEM WARM-UP 1
It took Dana 6 minutes to circle a quarter-mile track
three times. What was her average speed?
7½ mph. 3(1/4) = r(6/60)
WARM-UP 41
Algebra 2
WORD PROBLEM WARM-UP 1
A driver averaged a speed of 20 mph more for a trip
from A to B than on the return trip. The return trip
took one-and-a-half times as long. What was the
average speed from
a) A to B
b) B to A
a) 60 mph; b) 40 mph; D = rt = (r – 20)(3/2t)
WARM-UP 42
Algebra 2
WORD PROBLEM WARM-UP 1
A runner averaged 8 kph during a race. If she had
averaged 1 kph more, she would have finished in 20
minutes less. How long did it take her to finish the
race?
3 hours; D = 8t = (8 + 1)(t – 20/60)
WARM-UP 43
Algebra 2
WORD PROBLEM WARM-UP 1
A driver drove at 80 kph for 20 minutes of a 1 hour
trip. His average speed for the whole trip was 75
kph. What was his average speed for the other 40
minutes of the trip?
72-1/2 kph; D = 75(1) = 80(20/60) + r(40/60)
WARM-UP 44
Algebra 2
WORD PROBLEM WARM-UP 1
Nikita has already driven 1 mile at 30 mph. How
fast must she drive the second mile so that the
average speed for her trip is 60mph?
Answer: She cannot drive fast enough. She has
already used up all of her time.
WARM-UP 45
Algebra 2
WORD PROBLEM WARM-UP 1
Assume that all masons work at the same rate of
speed. If it takes eight masons (all working at the
same time) fifteen days to do a job, how long will it
take for the job to be done by ten masons?
8 masons x 15 days = 120 mason-days. Therefore
10 masons will take 12 days.
WARM-UP 46
Algebra 2
WORD PROBLEM WARM-UP 1
Suppose the amount of water that can flow through
two pipes is directly proportional to the squares of
their radii. Pipe A has a radius of 3 inches and water
flows through it at 150 gallons per second. At what
rate will water flow through Pipe B which has a
radius of 4 inches?
R=kr2. Therefore
WARM-UP 47
2 150 503 , so .
9 3k k
Algebra 2
WORD PROBLEM WARM-UP 1
Harold and Jem together can do a job in six days.
Harold can do the job working alone in eight days.
How long does it take Jem to do the job working
alone?
24 Days.
WARM-UP 48
1 1 1; 8
6H
H J
Algebra 2
WORD PROBLEM WARM-UP 1
It takes four minutes to fill a bathtub if the water is
full open and the drain is closed. It takes six
minutes to empty the tub if the drain is open and
the water is turned off. How long will it take to fill
the tub if the water is fully turned on and the drain
is open?
12 minutes
WARM-UP 49
1 1 14 6 m
Algebra 2
WORD PROBLEM WARM-UP 1
Two bricklayers working together can do a job in 8
days. One of the bricklayers takes 12 days to do the
job alone. How long does it take the other bricklayer
to do the job?
Answer: 24 days. Look at how much is accomplished per day. Together they complete 1/8 of the job in one day. One bricklayer would complete 1/12 of the job in one day. Therefore…1/8 – 1/12 = 1/24
WARM-UP 50
Algebra 2
WORD PROBLEM WARM-UP 1
A 15,000 gallon water tank can be filled in 20
minutes with two intake pipes, one of which allows
a 40% greater flow than the other. At what rate
does the water flow through each of the two pipes?
Answer A = 312.5 gpm & B = 437.5 gpm
pipe A + pipe B = 750 gallon/minute (gpm)Since pipe B = 1.40 A, we can say…1.00 A + 1.40 A = 750 gpmA = 312.5 gpm & B = 437.5 gpm
WARM-UP 51
Algebra 2
WORD PROBLEM WARM-UP 1
Jeff takes 40% longer than Ken to do a job. Jeff and
Ken working together can do the job in thirty-five
hours. How long does it take each of them working
alone to do the job?
WARM-UP 52
1.40
1 1 135
J K
J K