Ishibashi
Chabot College
Fall 2013
Math 104: Homework Exercises
Chapter 3: Applications
3.1 Perimeter
Find the perimeter of the given figure.
2.
1.
3 in
4 cm
5 cm
5 in
4 in
6 cm
7 in
3.
4.
3m
4 ft
5 ft
5m
6 ft
8m
5m
2 ft
7 ft
7m
Find the perimeter of each square using the formula P “ 4s.
5.
6.
7.
1m
8 ft
4 mi
4 mi
1m
8 ft
Find the perimeter of the each rectangle using the formula P “ 2` ` 2w.
8.
9.
10.
3 in
12 km
2 cm
10 km
7 cm
6 in
1
Find the perimeter of the each parallelogram using the formula P “ 2a ` 2b.
12.
11.
13.
15 m
5 in
15 m
7 in
4 ft
9 ft
3.2 Area
Find the area of the each square using the formula A “ s2 .
1.
2.
5 yd
3.
12 ft
2 cm
5 yd
12 ft
2 cm
Find the area of the each rectangle using the formula A “ `w.
4.
5.
6.
13 mi
2 km
5 ft
8 km
10 mi
4 ft
Find the area of the each parallelogram using the formula A “ bh.
7.
8.
9.
5 in
5 km
4 in
6 km
8 ft
11 ft
7 in
3 ft
3 km
2
Find the area of the each figure.
11.
10.
6 ft
2 mm
3 ft
5 mm
3 ft
4 mm
3 ft
6 ft
5 mm
12.
13.
5 yd
4 in
4 in
2 yd
4 in
3 in
6 yd
3 yd
10 in
2 yd
Find the area and perimeter of each figure.
14.
15.
5 mm
6m
7 mm
2m
7m
13 mm
2m
3.3 Solving Applications With One Unknown
Write the following as an algebraic expression with x as the variable.
1.
4 more than a number
2.
3 less than a number
3.
A number increased by 7
4.
2 subtracted from a number
5.
The sum of 1 and a number
6.
A number subtracted from 12
7.
The product of a number and 4
8.
A number multiplied by 9
9.
A number divided by 2
10.
Twice a number
11.
8 more than twice a number
12.
1 less than twice a number
13.
Three times a number
14.
Three times a number decreased by 4
3
15.
2 more than three times a number
16.
13 less than five times a number
Find the length of the missing side given the information provided.
17.
The perimeter is 31 ft.
18.
The area is 54 km2 .
9 km
?
7 ft
?
8 ft
5 ft
19.
The area is 36 in2 .
20.
The perimeter is 64 cm.
?
11 cm
6 in
4 in
18 cm
?
11 cm
16 cm
Solve each application problem.
21.
A number increased by 7 is 16. Find the number.
22.
When a number is subtracted from 12, the result
is 4. What is the number?
23.
When twice a number is increased by 8, the result
is 10 less than five times the number. What is the
number?
24.
If 13 less than five times a number is 1 less than
four times the number, what is the number?
25.
A square has perimeter 36 in. What is the length
of each side of the square?
26.
A triangle with three equal sides has perimeter 24
cm. What are the lengths of the sides?
Use a calculator to solve each application problem.
27.
John weighs 90 pounds less than twice Linda’s
weight. If John weighs 180 pounds, how much does
Linda weigh?
28.
A flight to Hawaii costs $205 more than three times
the cost of a flight to L.A. If a flight to Hawaii costs
$1180, how much does a trip to L.A. cost?
29.
Mike spent $15 less than three times what Vince
spent for dinner. If Mike spent $18 for dinner, how
much did Vance’s dinner cost?
30.
The Empire State Building is 76 feet less than twice
the height of Trump Tower. If the height of the Empire State Building is 1250 feet, what is the height
of Trump Tower?
4
3.4 Solving Applications With Two or More Unknowns
Express each unknown quantity using x as the only variable.
1.
Mark is 3 years older than Tommy.
2.
Mark’s age =
Tommy’s age =
3.
Skylar earns $16, 000 more per year than her
husband Walter.
Skylar’s income =
Walter’s income =
The length of a rectangle is twice its width.
4.
Length =
Width =
The longest side of a triangle is twice the length
of the shortest side. The third side is 3 ft longer
than the shortest side.
Shortest side =
Longest side =
Third side =
Solve each application problem.
5.
Mark is 3 years older than Tommy. If the sum of
their ages is 21, how old is each boy?
6.
Skylar earns $16, 000 more per year than her husband Walter. If their combined annual income is
$120, 000, how much does Skylar make per year?
7.
The number of men in a classroom is 7 less than
twice the number of women. If there are 56 people
in the classroom, how many men and women are
there?
8.
The number of Democrats in the California State
Senate is 4 less than three times the number of
Republicans. If there are 40 Senators, how many
are Democrats?
9.
The length of a rectangle is twice its width. If the
perimeter of the rectangle is 24 cm, what is the
length and width of the rectangle?
10.
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 40 inches, what
is the length and width of the rectangle?
11.
The length of a rectangular farm plot is 2 km less
than three times its width. If the perimeter is 20
km, what is the length of the longer side?
12.
A triangle has two sides of equal length. The third
side is 5 m longer than each of the other sides. If
the perimeter of the triangle is 23 m, what is the
length of the longer side?
13.
Trent has a bag of containing 20 red, green, and
blue marbles. The number of red marbles is 3 more
than the number of blue marbles. The number of
green marbles is 3 less than twice the number of
blue marbles. How many marbles of each color are
there?
14.
A triangle has three sides of different lengths. The
longest side is twice the length of the shortest side.
The third side is 3 ft longer than the shortest side.
If the perimeter of the triangle is 19 ft, what are
the lengths of the three sides?
Chapter 3 Review
Find the perimeter of each figure.
1.
2.
15 cm
2 ft
6 cm
8 ft
5 ft
9 cm
8 cm
9 ft
12 cm
5
Find the area and perimeter of each figure.
4.
3.
4 ft
16 cm
12 cm
6 ft
2 ft
15 cm
10 ft
Write the following as an algebraic expression with x as the variable.
5.
A number decreased by 8
6.
7 more than twice a number
7.
5 less than three times a number
8.
Five times a number increased by 2
Solve each application problem.
9.
If 4 less than three times a number is equal to twice
the number, what is the number?
10.
When 6 is subtracted from four times a number,
the result is the number plus 12. Find the number.
11.
The length of a rectangular building is 3 m more
than twice its width. If the distance around the
building is 42 m, what is the length and width of
the building?
12.
A rectangular garden is built in such a way that
the length of the garden is 1 foot less than three
times its width. If 30 feet of fencing is needed to
enclose the garden, what is the garden’s length and
width?
13.
The cost of a flat screen TV is four times more than
the cost of a DVD player. If the total cost is $850,
how much does each item cost?
14.
Carol has three daughters whose ages total 46. Jan
is 5 years older than Cindy while Marcia is 1 year
older than twice Cindy’s age. How old are the three
girls?
15.
Find the missing side of the figure below, given
that the perimeter is 33 cm.
16.
A hexagon is a figure with six sides. If the sides of
a hexagon are of equal length and the perimeter of
the hexagon is 48 feet, how long is each side?
7 cm
?
8 cm
9 cm
5 cm
6
Odd Answers to Exercises
3.1 Perimeter
1. 15 cm
3. 28 m
5. 16 mi
7. 4 m
9. 18 in
11. 24 in
13. 60 m
7. 28 in2
9. 18 km2
11. 36 ft2
13. 26 yd2
3.2 Area
1. 25 yd2
3. 144 ft2
5. 16 km2
15. A “ 22 m2
P “ 26 m
3.3 Solving Applications With One Unknown
1.
3.
5.
7.
x ` 4 or 4 ` x
x ` 7 or 7 ` x
1 ` x or x ` 1
4x
x
or x ˜ 2
9.
2
11.
13.
15.
17.
19.
21.
2x ` 8 or 8 ` 2x
3x
2 ` 3x or 3x ` 2
11 ft
9 in
9
23.
25.
27.
29.
6
9 in
135 pounds
$11
3.4 Solving Applications With Two or More Unknowns
1. Mark’s age = x ` 3
Tommy’s age = x
3. Length = 2x
Width = x
5. Mark’s age = 12 years
Tommy’s age = 9 years
7. Men = 35
Women = 21
9. Length = 8 cm
Width = 4 cm
11. 7 km
13. Red marbles = 8
Green marbles = 7
Blue marbles = 5
7. 3x ´ 5
9. 4
11. Length = 15 m
Width = 6 m
13. TV = $680
DVD Player = $170
15. 4 cm
Chapter 3 Review
1. 24 ft
3. A “ 180 cm2
P “ 62 cm
5. x ´ 8
7