Semester 1 Warm-Ups

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


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


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


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


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


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


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


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


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


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


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


15

7

( 7) 15

2 7 15

4

n d

n d

d d

d

d

Algebra 2


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


2

14

( 2) 14

2 2 14

8

q d

q d

d d

d

d

Algebra 2


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


3 10 5 2C C

Algebra 2


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


3( 5) 2A A

Algebra 2


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


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


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


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


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


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


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


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?


WARM-UP 22

40

2

( 2) 40

n d

d n

n n

Algebra 2


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?


WARM-UP 23

54

5( 3) 10 400 or

5 10 400 15

n d

n d

n d

Algebra 2


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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

Semester 1 Warm-Ups

Education

Transcript of Semester 1 Warm-Ups