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Math Problems
Grade 6
Evaluate variable expressions: word problems
The rectangular floor of a classroom is
36
36
36
feet in length and
39
39
39
feet in width. A scale drawing of the floor has a length of
12
12
12
inches. What is the area, in square inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
2
^{2}
2
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The rectangular floor of a classroom is
30
30
30
feet in length and
24
24
24
feet in width. A scale drawing of the floor has a length of
10
10
10
inches. What is the area, in square inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
2
^{2}
2
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Lisa is making a quilt using a scale of
1.5
1.5
1.5
inches
=
2
= 2
=
2
feet. Her scale drawing is
10.5
10.5
10.5
inches by
9
9
9
inches. What is the area, in square feet, of the actual quilt?
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According to a website where users review their doctors,
8
10
\frac{8}{10}
10
8
users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez's
1000
1000
1000
patients, about how many patients would recommend Dr. Gutierrez to their friends and family? (Round your answer to the nearest whole number.)
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A lock has a
3
3
3
-number code made up of
29
29
29
numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
\newline
Answer:
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Elmview School has an annual carnival. Each year, the school needs
2
b
+
18
2 b+18
2
b
+
18
balloons for carnival decorations, where
b
b
b
is the number of booths. Elmview has
12
12
12
booths planned for the carnival this year.
\newline
How many balloons does the school need to decorate for the carnival this year?
\newline
Write your answer as a whole number or decimal.
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A physical education teacher is planning to outline two adjacent identical rectangular areas for a new game that students will be learning. If the boundaries, including the center line, of this "court" must be marked with a single
50
50
50
-yard roll of tape, what is the maximum area of one of the smaller rectangular spaces, rounded to the nearest tenth of a square yard?
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If the radius of the large bubble is
5.7
c
m
5.7 \mathrm{~cm}
5.7
cm
, what is its circumference, in centimeters?
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The equation
8
x
−
6
y
=
1
8 x-6 y=1
8
x
−
6
y
=
1
is graphed in the
x
y
x y
x
y
-plane. What is the slope of the line?
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Six litres of white paint are mixed with three litres of blue paint that costs
$
2
\$ 2
$2
per litre more. The total price of the mixture is
$
24
\$ 24
$24
. Find the price of the white paint.
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Download
\newline
Page
\newline
11
11
11
\newline
of
58
58
58
\newline
7
7
7
−
22
-22
−
22
. Jillian is trying to construct an isosceles right triangle. She has started by constructing two perpendicular lines, as shown at right. If she wants each leg of the triangle to have length
a
a
a
as shown at right, describe how she should finish her construction.
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Nepal wants to have at least
250
250
250
Bengal tigers, Panthera tigris, within its borders by the year
2022
2022
2022
. As of
2009
2009
2009
, the population was
121
121
121
tigers. Naturalists have determined that
250
250
250
tigers would require
13500
13500
13500
square kilometers of territory. How much territory, in square kilometers, is needed for
121
121
121
tigers?
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Find the volume of a right circular cone that has a height of
11.8
f
t
11.8ft
11.8
f
t
and a base with a radius of
7.3
f
t
7.3ft
7.3
f
t
. Round your answer to the nearest tenth of a cubic foot.
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Complete the tables.
\newline
a.
\newline
\newline
| Yards | Feet |
\newline
|-------|------|
\newline
|
1
1
1
|
3
3
3
|
\newline
|
4
4
4
|
12
12
12
|
\newline
|
10
10
10
|
30
30
30
|
\newline
1
yard
=
3
feet
1 \text{ yard} = 3 \text{ feet}
1
yard
=
3
feet
. Multiply the number of yards by
3
3
3
to find the number of feet.
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in Costa Rica there is a tostadas food truck called miyas tostadas. This business is constantly high demand with a quene spanning an entire city block. If there are any remaining patrons in the line at closing time, they must be turned away and come back the next day. In this example let’s say about
1576
1576
1576
people visit the establishment per day to try to these tasty toasadas. They are open to
10
10
10
AM and close at
4
4
4
PM. We will assume that the customers enter at an equal rate for each hour they are open. They have the ability to serve around
225
225
225
customers per hour. How long does a customer arriving at
3.30
3.30
3.30
PM need to wait to be serviced? Answer should be expressed in minutes and you should round to the whole minute if needed
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The room is
20
20
20
feet wide and
35
35
35
feet long.
\newline
How much carpeting will you need to buy? Give your answer in
\newline
ft
2
\text{ft}^2
ft
2
.
\newline
How many feet of baseboard are needed? Give your answer in ft.
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John is comparing the fuel efficiency of three different car models: Model A, Model B, and Model C. The fuel efficiencies of the models are as follows: Model A:
25
mpg
25 \text{ mpg}
25
mpg
Model B:
30
mpg
30 \text{ mpg}
30
mpg
Model C:
20
mpg
20 \text{ mpg}
20
mpg
John plans to drive each car for a distance of
300
miles
300 \text{ miles}
300
miles
. If the cost of gasoline is
$
3.50
\$3.50
$3.50
per gallon, he wants to calculate the total cost of fuel for each model.
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How much will it cost to carpet a
25
ft
25 \text{ ft}
25
ft
by
13
ft
13 \text{ ft}
13
ft
room if carpeting costs
$
15.50
\$15.50
$15.50
per square yard?
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Yasmin was given a large box of
54
54
54
chocolates for her birthday. If she eats exactly
2
2
2
chocolates each day, how many chocolates would Yasmin have remaining
12
12
12
days after her birthday?
\newline
Answer:
□
\square
□
chocolates
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What is the volume of a sphere with a diameter of
8.2
8.2
8.2
i
n
\mathrm{in}
in
, rounded to the nearest tenth of a cubic inch?
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the side length of the base is
10
10
10
.
6
6
6
in
\text{in}
in
and the height of the pyramid is
14.9
14.9
14.9
i
n
\mathrm{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a right circular cone that has a height of
2
2
2
.
1
1
1
in
\text{in}
in
and a base with a diameter of
4
4
4
.
8
8
8
in
\text{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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If a recipe calls for
1
3
\frac{1}{3}
3
1
cup of sugar and you want to double the recipe, how many cups of sugar do you need in decimal form?
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Surface Area & Nets
6
6
6
GR
2
2
2
.
4
4
4
\newline
Find the surface area of the square pyramid using its net. The formula for each face is shown below.
\newline
(
4
)
(4)
(
4
)
28
28
28
square units
\newline
(
1
)
(1)
(
1
)
48
48
48
square units
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V= \text{type your answer}\cdot y\. \quad\text{cm}^{
3
3
3
}(\newline\)Account
\newline
2
2
2
\newline
1
1
1
point
\newline
Dashbuand
\newline
Workbook Question #
2
2
2
\newline
An oblique cylinder with a base of radius
2
2
2
units is shown. The top of the cylinder can be obtained by translating the base by the directed line segment
\newline
A
B
AB
A
B
which has length
\newline
6
2
6\sqrt{2}
6
2
units. The segment
\newline
A
B
AB
A
B
forms a
\newline
4
5
∘
45^{\circ}
4
5
∘
angle with the plane of the base. What is the volume of the cylinder? Round to the nearest
10
10
10
th
\newline
Calendar
\newline
2
2
2
\newline
1
1
1
\newline
3
3
3
\newline
2
2
2
\newline
4
4
4
\newline
5
5
5
\newline
Masten:
\newline
6
6
6
\newline
3
3
3
\newline
7
7
7
\newline
8
8
8
\newline
V=
106
106
106
.
9
9
9
\newline
\text{cm}^{
3
3
3
}
\newline
Resources
\newline
3
3
3
\newline
1
1
1
point
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What is the volume of a sphere with a diameter of
6
6
6
.
3
3
3
in
\text{in}
in
, rounded to the nearest tenth of a cubic inch?
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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What is the volume of a sphere with a radius of
53.9
53.9
53.9
i
n
\mathrm{in}
in
, rounded to the nearest tenth of a cubic inch?
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Aisha is working two summer jobs, making
$
9
\$ 9
$9
per hour washing cars and making
$
25
\$ 25
$25
per hour tutoring. In a given week, she can work a maximum of
18
18
18
total hours and must earn a minimum of
$
290
\$ 290
$290
. If Aisha worked
3
3
3
hours washing cars, determine the maximum number of whole hours tutoring that she can work and still meet her requirements.
\newline
Answer:
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Mason has some nickels and some dimes. He has a minimum of
15
15
15
coins worth at most
$
1
\$ 1
$1
combined. If Mason has
3
3
3
dimes, determine the maximum number of nickels that he could have.
\newline
Answer:
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Stella has some nickels and some dimes. She has a minimum of
15
15
15
coins worth no more than
$
1.25
\$ 1.25
$1.25
combined. If Stella has
11
11
11
nickels, determine the maximum number of dimes that she could have.
\newline
Answer:
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for
$
7.50
\$ 7.50
$7.50
and each adult ticket sells for
$
10
\$ 10
$10
. The auditorium can hold a maximum of
134
134
134
people. The drama club must make a minimum of
$
1200
\$ 1200
$1200
from ticket sales to cover the show's costs. If
85
85
85
adult tickets were sold, determine all possible values for the number of student tickets that the drama club must sell in order to meet the show's expenses.
\newline
Answer:
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Roselyn is driving to visit her family, who live
150
150
150
kilometers away. Her average speed is
60
60
60
kilometers per hour. The car's tank has
20
20
20
liters of fuel at the beginning of the drive, and its fuel efficiency is
6
6
6
kilometers per liter. Fuel costs
.
6
.6
.6
dollars per liter. What is the price for the amount of fuel that Roselyn will use for the entire drive?
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A
6
6
6
-inch candle burns down in
4
4
4
hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a
4
1
2
4 \frac{1}{2}
4
2
1
-inch candle to burn down?
\newline
Answer: hours
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The lengths of the three sides of a triangle (in meters) are consecutive integers. If the perimeter is
48
48
48
meters, find the value of the longest of the three side lengths.
\newline
Answer: meters
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The lengths of the four sides of a quadrilateral (in centimeters) are consecutive integers. If the perimeter is
126
126
126
centimeters, find the value of the shortest of the four side lengths.
\newline
Answer: centimeters
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The lengths of the four sides of a quadrilateral (in centimeters) are consecutive integers. If the perimeter is
46
46
46
centimeters, find the value of the longest of the four side lengths.
\newline
Answer: centimeters
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The lengths of the three sides of a triangle (in meters) are consecutive odd integers. If the perimeter is
93
93
93
meters, find the value of the shortest of the three side lengths.
\newline
Answer: meters
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The lengths of the three sides of a triangle (in inches) are consecutive integers. If the perimeter is
75
75
75
inches, find the value of the middle of the three side lengths.
\newline
Answer: inches
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The lengths of the three sides of a triangle (in meters) are consecutive even integers. If the perimeter is
96
96
96
meters, find the value of the shortest of the three side lengths.
\newline
Answer: meters
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A man starts walking north at
2
ft/s
2\,\text{ft/s}
2
ft/s
from a point
P
P
P
. Five minutes later a woman starts walking south at
5
ft/s
5\,\text{ft/s}
5
ft/s
from a point
500
ft
500\,\text{ft}
500
ft
due east of
P
P
P
. At what rate are the woman and man separating when the woman starts walking? (Round your answer to two decimal places.)
\newline
Enter a number:______
ft/s
\text{ft/s}
ft/s
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Find the volume of a right circular cone that has a height of
11
11
11
.
2
2
2
in
\text{in}
in
and a base with a circumference of
12
12
12
.
6
6
6
in
\text{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a right circular cone that has a height of
11
11
11
.
7
7
7
in
\text{in}
in
and a base with a circumference of
18.8
18.8
18.8
i
n
\mathrm{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
9
f
t
9 \mathrm{ft}
9
ft
and the height of the pyramid is
6.4
f
t
6.4 \mathrm{ft}
6.4
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the area of the base is
16.6
i
n
2
16.6 \mathrm{in}^{2}
16.6
in
2
and the height of the pyramid is
20.9
i
n
20.9 \mathrm{in}
20.9
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the area of the base is
7.7
m
2
7.7 \mathrm{~m}^{2}
7.7
m
2
and the height of the pyramid is
4.2
m
4.2 \mathrm{~m}
4.2
m
. Round your answer to the nearest tenth of a cubic meter.
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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Find the volume of a pyramid with a square base, where the area of the base is
19.3
f
t
2
19.3 \mathrm{ft}^{2}
19.3
ft
2
and the height of the pyramid is
25.3
f
t
25.3 \mathrm{ft}
25.3
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the side length of the base is
18
18
18
.
2
2
2
in and the height of the pyramid is
12.2
i
n
12.2 \mathrm{in}
12.2
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the side length of the base is
13
13
13
.
2
2
2
in and the height of the pyramid is
7.3
i
n
7.3 \mathrm{in}
7.3
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
4.2
f
t
4.2 \mathrm{ft}
4.2
ft
and the height of the pyramid is
4.7
f
t
4.7 \mathrm{ft}
4.7
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
9.4
f
t
9.4 \mathrm{ft}
9.4
ft
and the height of the pyramid is
6.2
f
t
6.2 \mathrm{ft}
6.2
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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