This document contains 33 word problems involving algebra concepts like equations, inequalities, functions, and geometry. The problems cover a range of difficulty levels and topics including age word problems, coin word problems, perimeter and area problems, and other algebraic reasoning questions. Students are asked to solve each problem and show the step-by-step work.

1. Algebra 2
WARM-UP 1 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.

2. Algebra 2
WARM-UP 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).

3. Algebra 2
WARM-UP 3 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.

4. Algebra 2
WARM-UP 4 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.

5. Algebra 2
WARM-UP 5 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.

6. Algebra 2
WARM-UP 6 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

7. Algebra 2
WARM-UP 7WORD 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.

8. Algebra 2
WARM-UP 8
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.

9. Algebra 2
WARM-UP 9WORD PROBLEM WARM-UP 1
A box of 100 personalized pencils costs $30. How many
dollars does it cost to buy 2500 pencils?
Answer: $750.

10. Algebra 2
WARM-UP 10 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? If x  y = 6 and x + y = 12, what is the value of
y?
Answer: 12 coins.

11. Algebra 2
WARM-UP 11 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.
If x  y = 6 and x + y = 12, what is the value of
y?
n  d  15
n d 7
(d  7)  d  15
2d  7  15
d 4

12. Algebra 2
WARM-UP 12 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. q d 2
If x  y = 6 and x + y = 12, what is the value of
y?
q  d  14
(d  2)  d  14
2d  2  14
d 8

13. Algebra 2
WARM-UP 13 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. 3C  10  5C  2
If x  y = 6 and x + y = 12, what is the value of
y?

14. Algebra 2
WARM-UP 14 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. 3(A  5)  2A
If x  y = 6 and x + y = 12, what is the value of
y?

15. Algebra 2
WARM-UP 15 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.
G V  23
G V  7
V  (V  7)  23
V
2  7  23

16. Algebra 2
WARM-UP 16 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.
B  L 5
B  L  31
(L  5)  L  31
2L  5  31

17. Algebra 2
WARM-UP 17 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.
J H  24
J  2H
(2H )  H  24
3H  24

18. Algebra 2
WARM-UP 18 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.
E  5  2F
E 3  F
E  5  2(E  3)
E  5  2E  6

19. Algebra 2
WARM-UP 19 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.
2L  5  3(L  1)
2L  5  3L  3
8L

20. Algebra 2
WARM-UP 20 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.
2L  5  3(L  1)
2L  5  3L  3

21. Algebra 2
WARM-UP 21 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.
n  d  37
10d  5n  40
n
n  4  37
2

22. Algebra 2
WARM-UP 22 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.
n  d  40
d n 2
n  (n  2)  40

23. Algebra 2
WARM-UP 23 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.
n  d  54
5(n  3)  10d  400 or
5n  10d  400  15

24. Algebra 2
WARM-UP 24 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.
n d 2
d q 5
5n  10d  25q  325

25. Algebra 2
WARM-UP 25 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.
n  3d
p  5n
p  5n  10d  280

26. Algebra 2
WARM-UP 26 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.
n  3d
p  5n
p  5n  10d  280

27. Algebra 2
WARM-UP 27 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
P  2w  2l
P  2w  2(w  5)
P  4w  10

28. Algebra 2
WARM-UP 28 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: a. A  15  (b  6)(c  2)
b. 2A  (b  6)(c  2)

29. Algebra 2
WARM-UP 29 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

30. Algebra 2
WARM-UP 30 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: a. A  40  (l  5)w
2 2
b. A  l
3

31. Algebra 2
WARM-UP 31 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
A  lw
(.25l )(.80w )  .2(lw )  .20A

32. Algebra 2
WARM-UP 32 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
P  2(l  w )
w  P  40
102  lw

33. Algebra 2
WARM-UP 33 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
l w 3
A  lw
A  30  (l  2)w

34. Algebra 2
WARM-UP 34
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
D  rt
sumof distances
average speed=
sumof times
D  40(3); D  50(2)
1 2

35. Algebra 2
WARM-UP 35 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: 65 5 mph
27
sumofdistances
a  average speed=
sumof times
D D 2(D  D )
a 1
; a 
2 1 2
t t
1 2
t t t
1 2 3

36. Algebra 2
WARM-UP 36 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

37. Algebra 2
WARM-UP 37 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)

38. Algebra 2
WARM-UP 38 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

39. Algebra 2
WARM-UP 39 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)

40. Algebra 2
WARM-UP 40 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)

41. Algebra 2
WARM-UP 41 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)

42. Algebra 2
WARM-UP 42 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)

43. Algebra 2
WARM-UP 43 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)

44. Algebra 2
WARM-UP 44 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)

45. Algebra 2
WARM-UP 45 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.

46. Algebra 2
WARM-UP 46 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.

47. Algebra 2
WARM-UP 47 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=kr  
2. Therefore k 32 , so k  150  50 .
9 3

48. Algebra 2
WARM-UP 48 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.
1 1 1
  ; H 8
H J 6

49. Algebra 2
WARM-UP 49 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?
1 1 1
12 minutes  
4 6 m

50. Algebra 2
WARM-UP 50 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

51. Algebra 2
WARM-UP 51 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 gpm
A = 312.5 gpm & B = 437.5 gpm

52. Algebra 2
WARM-UP 52
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?
J  1.40K
1 1 1
 
J K 35