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Math Problems
Grade 6
Evaluate variable expressions: word problems
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
0.60
0.60
0.60
dollars per liter.
\newline
What is the price for the amount of fuel that Roselyn will use for the entire drive?
\newline
□
\square
□
dollars
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Francine uses
2
3
\frac{2}{3}
3
2
cup of pineapple juice for every
1
3
\frac{1}{3}
3
1
cup of orange juice to make a smoothie.
\newline
Enter the number of cups of pineapple juice Francine uses for
1
1
1
cup of orange juice.
\newline
□
\square
□
cups of pineapple juice
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Base of a triangle is
9
9
9
and height is
5
5
5
. Base of another triangle is
10
10
10
and height is
6
6
6
. Find the ratio of areas of these triangles.
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The cost of a certain number of pens is ₹
72
72
72
. If the cost of each pen is decreased by ₹
1
1
1
, then
8
8
8
more pens can be purchased for the same amount. How many pens can be purchased for the same amount if the cost of each pen is increased by ₹
1
1
1
.
50
50
50
?
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Points
A
,
B
A, B
A
,
B
and
C
C
C
lie on a circle with center
Q
Q
Q
.
\newline
- The area of sector
A
Q
B
\mathrm{AQB}
AQB
is twice the area of sector
B
Q
C
\mathrm{BQC}
BQC
.
\newline
- The length of arc
A
B
\mathrm{AB}
AB
is
28
28
28
centimeters.
\newline
What is the length, in centimeters, of
arc
B
C
\operatorname{arc} B C
arc
BC
?
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What is the total number of different
9
9
9
-letter arrangements that can be formed using the letters in the word CHICANERY?
\newline
Answer:
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What is the total number of different
11
11
11
-letter arrangements that can be formed using the letters in the word MEASUREMENT?
\newline
Answer:
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A winning class group prize pays
$
1600
\$ 1600
$1600
.
\newline
This is shared between Peter and Mary in ratio
3
3
3
:
5
5
5
.
\newline
How much money does Peter get?
\newline
(Answer format to include
$
\$
$
)
\newline
□
\square
□
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Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of
24
24
24
points and made
2
2
2
more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made,
x
x
x
, and the number of three point shots made,
y
y
y
.
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Pete's dad ordered
32
32
32
donuts for Pete's birthday party at school. Pete's classmates ate
24
24
24
donuts. Pete will eat the remaining donuts at home, but is only allowed to have
2
2
2
per day.
\newline
Complete the expression below to show how many days it will take Pete to eat the leftover donuts.
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Another garden is in the shape of a semicircle with a radius of
25
25
25
feet. Edging is placed around this garden.
\newline
How much edging, in feet, is needed to go around this garden? Round to the nearest whole number.
\newline
Enter your answer in the box.
\newline
□
\square
□
feet
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Kenny will be away at a basketball camp, and a outdoors camp during the summer. The total time he will be away is
8
8
8
weeks.
\newline
If his basketball camp is
21
21
21
days long, how many days long is the outdoors camp?
\newline
(A)
35
35
35
\newline
(B)
42
42
42
\newline
(C)
56
56
56
\newline
(D)
5
5
5
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Angela is building a pool that is
25
25
25
meters long. She has selected tiles to put around the edge of the pool. If each tile is
8
8
8
inches long, how many tiles does she need for one
25
25
25
-meter side of the pool?
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Your ceiling is
210
\mathbf{2 1 0}
210
centimetres high, You want the tree to have
30
\mathbf{3 0}
30
centimetres of space with the ceiling. How tall must the tree be? (in centimetres)
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Hailey paid
$
13
\$13
$13
for
1
3
7
1\dfrac{3}{7}
1
7
3
kg
\text{kg}
kg
of sliced salami. What was the cost per kilogram of salami
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An aquarium can be modeled as a right rectangular prism and it can hold
882
882
882
cubic inches of water when it is full. Its width is
7
7
7
in and height is
7
7
7
in. Find the length of the aquarium in inches. Round your answer to the nearest tenth if necessary.
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Luis models the volume of a popcorn box as a right rectangular prism. Its dimensions are
3
1
2
3 \frac{1}{2}
3
2
1
in by
2
2
2
in by
6
3
4
6 \frac{3}{4}
6
4
3
in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.
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The coordinates of the point
J
J
J
are
(
4
,
5
)
(4,5)
(
4
,
5
)
and the coordinates of point
K
K
K
are
(
9
,
5
)
(9,5)
(
9
,
5
)
. What is the distance, in units, between the point
J
J
J
and point
K
K
K
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
T
T
T
are
(
−
5
,
−
8
)
(-5,-8)
(
−
5
,
−
8
)
and the coordinates of point
U
U
U
are
(
−
5
,
−
2
)
(-5,-2)
(
−
5
,
−
2
)
. What is the distance, in units, between the point
T
T
T
and point
U
?
U ?
U
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
P
P
P
are
(
0
,
7
)
(0,7)
(
0
,
7
)
and the coordinates of point
Q
Q
Q
are
(
5
,
7
)
(5,7)
(
5
,
7
)
. What is the distance, in units, between the point
P
P
P
and point
Q
Q
Q
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
T
T
T
are
(
10
,
9
)
(10,9)
(
10
,
9
)
and the coordinates of point
U
U
U
are
(
−
2
,
9
)
(-2,9)
(
−
2
,
9
)
. What is the distance, in units, between the point
T
T
T
and point
U
U
U
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
P
P
P
are
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
and the coordinates of point
Q
Q
Q
are
(
10
,
−
1
)
(10,-1)
(
10
,
−
1
)
. What is the distance, in units, between the point
P
P
P
and point
Q
?
Q ?
Q
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
F
F
F
are
(
2
,
−
6
)
(2,-6)
(
2
,
−
6
)
and the coordinates of point
G
G
G
are
(
−
4
,
−
6
)
(-4,-6)
(
−
4
,
−
6
)
. What is the distance, in units, between the point
F
F
F
and point
G
?
G ?
G
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
K
K
K
are
(
−
5
,
8
)
(-5,8)
(
−
5
,
8
)
and the coordinates of point
L
L
L
are
(
−
5
,
−
6
)
(-5,-6)
(
−
5
,
−
6
)
. What is the distance, in units, between the point
K
K
K
and point
L
L
L
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
J
J
J
are
(
0
,
−
10
)
(0,-10)
(
0
,
−
10
)
and the coordinates of point
K
K
K
are
(
7
,
−
10
)
(7,-10)
(
7
,
−
10
)
. What is the distance, in units, between the point
J
J
J
and point
K
?
K ?
K
?
\newline
Answer:
□
\square
□
units
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The coordinates of the point
O
O
O
are
(
3
,
−
5
)
(3,-5)
(
3
,
−
5
)
and the coordinates of point
P
P
P
are
(
8
,
−
5
)
(8,-5)
(
8
,
−
5
)
. What is the distance, in units, between the point
O
O
O
and point
P
P
P
?
\newline
Answer:
□
\square
□
units
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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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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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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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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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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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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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