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Math Problems
Grade 7
GCF and LCM: word problems
OHeady
\newline
Practice: GCF and LCM - Quiz - Level F
\newline
Mrs. Flossi is hosting a trivia contest for
40
40
40
students and
24
24
24
staff members. Tc Mrs. Flossi wants there to be the same number of students and the same num staff members on each team.
\newline
What is the greatest number of teams Mrs. Flossi can make?
\newline
3
3
3
teams
\newline
4
4
4
teams
\newline
5
5
5
teams
\newline
8
8
8
teams
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Alonzo's Bakery is giving a treat to each customer at a grand opening event. Each customer spins a wheel to determine which treat they get. Every customer has a
32
%
32 \%
32%
chance of getting a cupcake, a
52
%
52 \%
52%
chance of getting a brownie, and a
16
%
16 \%
16%
chance of getting a muffin.
\newline
Alonzo wants to simulate what could happen for the first ten customers.
\newline
So for each customer, he generates a random whole number from
1
1
1
to
100
100
100
.
\newline
(a) What is a range of values that Alonzo can use to represent a customer getting a brownie?
\newline
□
\square
□
to
□
\square
□
\newline
(b) Here is Alonzo's simulation.
\newline
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}
\newline
\hline Customer &
1
1
1
&
2
2
2
&
3
3
3
&
4
4
4
&
5
5
5
&
6
6
6
&
7
7
7
&
8
8
8
&
9
9
9
&
10
10
10
\\
\newline
\hline Random number &
48
48
48
&
83
83
83
&
1
1
1
&
53
53
53
&
52
52
52
&
23
23
23
&
8
8
8
&
10
10
10
&
37
37
37
&
85
85
85
\\
\newline
\hline
\newline
\end{tabular}
\newline
Using your answer in part (a), find the percentage of the
10
10
10
simulated customers who got a brownie.
\newline
□
\square
□
%
\%
%
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A
7
7
7
-year
$
1
,
000
\$1,000
$1
,
000
bond has coupons paid quarterly at a rate of
9
%
9\%
9%
. The bond can be redeemed early in
3
3
3
years at a price of
$
1
,
070
\$1,070
$1
,
070
. If the bond is valued at
$
900
\$900
$900
, what is the highest and lowest return an investor can get and under what conditions?
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In an examination of three subjects, out of
260
260
260
students,
190
190
190
passed in English,
60
60
60
in Maths and
75
75
75
in Science. For every person who failed only in English, there were
2
2
2
person who failed only in science and
3
3
3
who failed in Maths alone. The number of students who passed in exactly two subjects was
5
5
5
more than the number of students who passes in all three. Also, those who passed in English along with only one other subject were equal in number to those who passed all three subjects. Find the number of students who failed in all the three subjects.
\newline
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47
47
47
.
\newline
A member of the Cherokee Nation, Mary Golda Ross is renowned for her contributions to NASA's Planetary Flight Handbook, which
\qquad
detailed mathematical guidance for missions to Mars and Venus.
\newline
Which choice completes the text so that it conforms to the conventions of Standard English?
\newline
A. provided
\newline
B. having provided
\newline
C. to provide
\newline
D. providing
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In a sports league each team has
27
27
27
players and
6
6
6
coaches. There are also a number of team assistants. The ratio of team assistants to players is
2
:
3
2:3
2
:
3
. What is the ratio of coaches to assistants?
\newline
A.
1
/
3
1/3
1/3
\newline
B.
2
/
3
2/3
2/3
\newline
C.
3
/
2
3/2
3/2
\newline
D.
3
3
3
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Elizabeth and her children went into a movie theater where they sell bags of popcorn for
$
7.50
\$7.50
$7.50
each and pretzels for
$
4.50
\$4.50
$4.50
each. Elizabeth has
$
120
\$120
$120
to spend and must buy at least
18
18
18
bags of popcorn and pretzels altogether. If Elizabeth decided to buy
7
7
7
bags of popcorn, determine all possible values for the number of pretzels that she could buy.
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Mari has
39
39
39
square feet of patio bricks to put around the edge of a rectangular garden. Each square brick has sides that are
1
1
1
foot long. What is the greatest perimeter that she can make with the bricks?
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A box contains
4
4
4
red cards,
6
6
6
blue cards, and
10
10
10
green cards. What is the smallest number of cards we must remove from the box to make sure that we have
2
2
2
cards of the same color?
\newline
E.
2
2
2
\newline
F.
3
3
3
\newline
G.
4
4
4
\newline
H.
17
17
17
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In a certain high school, there were
6
6
6
students who were not old enough to vote for every
1
1
1
student who was old enough to vote. If there were
840
840
840
students in the school, how many students were old enough to vote?
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Sam and Temmy open their ice cream shop everyday during warm months but only open their ice cream shops during the weekends when the weather is cool. They have been keeping records for the first
14
14
14
monthis. They want to know an equation that can predict their second year of income
\newline
- Form an equation. in the Make model for their patterns of income, different parts of the year/
2
2
2
nd year.
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A travel agency is planning a holiday for a group of people. The agency receives quotations from two coach companies, Maya Express and Great Holidays. Maya Express charges
$
15
\$ 15
$15
for each person while Great Holidays charges
$
12
\$ 12
$12
per person and a separate fee of
$
84
\$ 84
$84
. If the total amount charged by each company is the same, find the number of people going on the holiday.
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1
1
1
.
1
1
1
irrational numbers
\newline
10
10
10
a Use a calculator to find
i
i
i
\newline
(
2
+
1
)
×
(
2
−
1
)
(\sqrt{2}+1)\times(\sqrt{2}-1)
(
2
+
1
)
×
(
2
−
1
)
\newline
b Continue the pattern of
i
i
ii
ii
\newline
(
3
+
1
)
×
(
3
−
1
)
(\sqrt{3}+1)\times(\sqrt{3}-1)
(
3
+
1
)
×
(
3
−
1
)
\newline
c Generalise the restern of the multiplications in part a.
\newline
d Check your the results to find
\newline
(
N
+
1
)
×
(
N
−
1
)
(\sqrt{N}+1)\times(\sqrt{N}-1)
(
N
+
1
)
×
(
N
−
1
)
where
\newline
N
N
N
is a positive integer.
\newline
11
11
11
Here is a decim generalisation with further examples.
\newline
Arun says:
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There are
36
36
36
children participating at a chess tournament. The tournament consist of
3
3
3
rounds (Preliminary, Semifinal, and Final). In each round, half of the participants are eliminated. After the Simifinal round, how many participants are left to compete in the Final round?
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There were
90
90
90
marbles in
3
3
3
bags,
P
P
P
,
Q
Q
Q
, and
R
R
R
. Jane moved
6
6
6
marbles from Bag
P
P
P
to Bag
Q
Q
Q
and
5
5
5
marbles from Bag
Q
Q
Q
to Bag
R
R
R
. He then moved
3
3
3
1
1
1
marbles from Bag
R
R
R
to Bag
P
P
P
. There were an equal number of marbles in each bag in the end. How many marbles were there in Bag
Q
Q
Q
at first?
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Jose tracks how many times he got fast food each month. He got fast food
12
12
12
times in January,
10
10
10
times in February,
18
18
18
times in March,
4
4
4
times in April, and
2
2
2
times in May.
\newline
Find the mean number of times Jose got fast food.
\newline
□
\square
□
times getting fast food
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Sara has
16
16
16
red flowers and
28
28
28
yellow flowers. She wants to make bouquets with the same number of each color flower in each Bouquet. What is the greatest number of bouquets she can make
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Ruby can assemble
2
2
2
gift baskets by herself in
7
7
7
minutes. Emma can assemble
4
4
4
gift baskets by herself in
15
15
15
minutes. Ruby begins assembling gift baskets at
1
1
1
:
00
00
00
p.m., and Emma begins assembling gift baskets at
1
:
15
1: 15
1
:
15
p.m. If they continue to work at the above rates, at what time will they finish the
5
4
th
54^{\text {th }}
5
4
th
basket?
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One travel association claims that each US household saves an average of
$
1148
\$ 1148
$1148
in taxes because of the tax revenue generated by leisure and business travel. Suppose there is a ratio of
$
9
:
$
19
\$ 9: \$ 19
$9
:
$19
between tax revenue generated by business travel and by leisure travel. How many dollars would the average US household save in taxes because of the tax revenue generated by business travel?
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Hamadi is renting a car. The rental charge is
$
17.50
\$ 17.50
$17.50
per day plus
$
0.16
\$ 0.16
$0.16
per mile. Hamadi can spend at most
$
33
\$ 33
$33
for the cost of the car rental. If Hamadi rents the car for one day, which of the following is one possible number of miles Hamadi can drive the rental car?
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Find the sum of all positive integers
n
n
n
such that, given an unlimited supply of stamps of denominations
5
5
5
,
n
n
n
, and
n
+
1
n+1
n
+
1
cents,
91
91
91
cents is the greatest postage that cannot be formed.
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A market research group conducted a survey of
1000
1000
1000
consumers and reported that
720
720
720
consumers liked the product
A
A
A
and
450
450
450
consumers liked product B. What is the least number that must have liked both products?
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IN a Cartain exmimation,
72
72
72
candidates opz ered methenatics,
64
64
64
affered finglish and
G
2
G_{2}
G
2
French,
18
18
18
afianed
5
5
5
oth makremales ind Inglish,
24
24
24
mathematies and French and
20
20
20
-Cuglish and erench.
8
8
8
Gndidates eppered rll the three sublects. How mary Cindidates where there For the examintion?
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IN a Cartain exmimation,
72
72
72
candidates ofzered methenatics,
64
64
64
affered finglish and
G
2
G_{2}
G
2
French,
18
18
18
afianed
5
5
5
oth makremales ind Inglish,
24
24
24
mathematies and French and
20
20
20
-Cuglish and erench.
8
8
8
Gndidates eppered rll the three sublects. How mary Cindidates where there For the examintion?
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In a certain examination,
72
72
72
candidates offered mathematics,
64
64
64
offered English and
G
2
G_{2}
G
2
French.
18
18
18
offered both mathematics and English,
24
24
24
mathematics and French, and
20
20
20
- English and French.
8
8
8
candidates offered all the three subjects. How many candidates were there?
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Erik is doing upper body workouts in an attempt to get stronger. At the he sees how many push-ups he can do with good form until he is exhaust done
7
7
7
sets with the following numbers of push-ups:
\newline
8
8
8
push-ups
\newline
5
5
5
push-ups
\newline
6
6
6
push-ups
\newline
9
9
9
push-ups
\newline
7
7
7
push-ups
\newline
8
8
8
pus
\newline
What was the mean number of push-ups Erik performed?
\newline
____push-ups
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An aquarium is designing a new exhibit to showcase tropical fish. The exhibit will include a tank that is a rectangular prism with a length,
l
l
l
, that is twice the width,
w
w
w
. The volume of the tank is
420
420
420
cubic feet. What is the width of the tank to the nearest tenth of a foot?
\newline
Hint: There is another way to represent the length of the tank in terms other than
l
l
l
.
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During her last road trip, Sophia drove
402
402
402
miles on
12
12
12
gallons of gas. Sophia's car averages
37
37
37
miles per gallon (mpg) on highways and
25
25
25
mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?
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A group of
4
4
4
friends is playing cards. The deck has
70
70
70
cards. To start the game, the dealer makes a pile of
15
15
15
cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone.
\newline
What is the greatest number of cards any player will have after all the cards are dealt?
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Meena and her children went into a grocery store where they sell bananas for
$
0.70
\$ 0.70
$0.70
each and mangos for
$
1.50
\$ 1.50
$1.50
each. Meena has
$
15
\$ 15
$15
to spend and must buy no less than
10
10
10
bananas and mangos altogether. If Meena decided to buy
6
6
6
mangos, determine the maximum number of bananas that she could buy.
\newline
Answer:
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Elijah and his children went into a grocery store where they sell apples for
$
1.50
\$ 1.50
$1.50
each and peaches for
$
2
\$ 2
$2
each. Elijah has
$
20
\$ 20
$20
to spend and must buy at least
10
10
10
apples and peaches altogether. If Elijah decided to buy
6
6
6
apples, determine the maximum number of peaches that he could buy.
\newline
Answer:
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Joshua owns a food truck that sells tacos and burritos. He only has enough supplies to make
96
96
96
tacos or burritos. He sells each taco for
$
3.75
\$ 3.75
$3.75
and each burrito for
$
7.50
\$ 7.50
$7.50
. Joshua must sell a minimum of
$
600
\$ 600
$600
worth of tacos and burritos each day. If
65
65
65
burritos were sold, determine the minimum number of tacos that the Joshua must sell in order to meet the requirements.
\newline
Answer:
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An online furniture store sells chairs for
$
50
\$ 50
$50
each and tables for
$
250
\$ 250
$250
each. Every day, the store can ship no more than
44
44
44
pieces of furniture and must sell a minimum of
$
6000
\$ 6000
$6000
worth of chairs and tables. If
28
28
28
chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.
\newline
Answer:
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Hawa is working two summer jobs, making
$
9
\$ 9
$9
per hour babysitting and making
$
13
\$ 13
$13
per hour tutoring. In a given week, she can work no more than
12
12
12
total hours and must earn a minimum of
$
120
\$ 120
$120
. If Hawa worked
2
2
2
hours babysitting, determine the minimum number of whole hours tutoring that she must work to meet her requirements.
\newline
Answer:
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Madelyn and her children went into a restaurant where they sell hamburgers for
$
6
\$ 6
$6
each and tacos for
$
4
\$ 4
$4
each. Madelyn has
$
60
\$ 60
$60
to spend and must buy a minimum of
12
12
12
hamburgers and tacos altogether. If Madelyn decided to buy
4
4
4
hamburgers, determine the maximum number of tacos that she could buy.
\newline
Answer:
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Brody and his children went into a restaurant where they sell hamburgers for
$
5
\$ 5
$5
each and tacos for
$
2.50
\$ 2.50
$2.50
each. Brody has
$
60
\$ 60
$60
to spend and must buy no less than
14
14
14
hamburgers and tacos altogether. If Brody decided to buy
7
7
7
hamburgers, determine all possible values for the number of tacos that he could buy.
\newline
Answer:
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Nayeli is working two summer jobs, making
$
6
\$ 6
$6
per hour walking dogs and making
$
12
\$ 12
$12
per hour landscaping. In a given week, she can work no more than
15
15
15
total hours and must earn no less than
$
120
\$ 120
$120
. If Nayeli worked
3
3
3
hours walking dogs, determine the minimum number of whole hours landscaping that she must work to meet her requirements.
\newline
Answer:
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An online furniture store sells chairs for
$
100
\$ 100
$100
each and tables for
$
350
\$ 350
$350
each. Every day, the store can ship at most
33
33
33
pieces of furniture and must sell at least
$
5800
\$ 5800
$5800
worth of chairs and tables. If
20
20
20
chairs were sold, determine the maximum number of tables that the store could sell that would meet the requirements.
\newline
Answer:
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Savannah is working two summer jobs, making
$
10
\$ 10
$10
per hour washing cars and making
$
18
\$18
$18
per hour tutoring. In a given week, she can work at most
12
12
12
total hours and must earn a minimum of
$
160
\$ 160
$160
. If Savannah worked
7
7
7
hours tutoring, determine all possible values for the number of whole hours washing cars that she must work to meet her requirements.
\newline
Answer:
□
\square
□
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A small airplane can carry passengers, luggage, and mail as long as their total weight is less than
1
,
700
1,700
1
,
700
pounds. Tuesday's load of mail weighs
490
490
490
pounds. If the average combined weight of each passenger and their luggage is
170
170
170
pounds, what is the greatest possible number of passengers that can travel on the airplane on Tuesday?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
\newline
(B)
8
8
8
\newline
(C)
10
10
10
\newline
(D)
12
12
12
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A
3
3
3
-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of
8
8
8
inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie?
\newline
A.
24
24
24
\newline
B.
64
64
64
\newline
C.
72
72
72
\newline
D.
192
192
192
\newline
E.
512
512
512
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Carol, the band director, tracked how many minutes each saxophone player practiced last week. She found that Sven practiced for
30
30
30
minutes, Li Mihn practiced for
45
45
45
minutes, Wendy practiced for
90
90
90
minutes, Thomas practiced for
75
75
75
minutes, and Gabriel practiced for
60
60
60
minutes.
\newline
Find the mean length of practice time.
\newline
minutes
\text{minutes}
minutes
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Carol, the band director, tracked how many minutes each saxophone player practiced last week. She found that Sven practiced for
30
30
30
minutes, Li Mihn practiced for
45
45
45
minutes, Wendy practiced for
90
90
90
minutes, Thomas practiced for
75
75
75
minutes, and Gabriel practiced for
60
60
60
minutes.
\newline
Find the mean length of practice time.
\newline
□
\square
□
minutes
\text{minutes}
minutes
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A scale on a map shows that
3
3
3
centimeters represents
10
10
10
kilometers.
\newline
What number of centimeters on the map represents an actual distance of
25
25
25
kilometers?
\newline
centimeters
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Darcy harvests
8
3
4
8 \frac{3}{4}
8
4
3
acres of corn every
5
6
\frac{5}{6}
6
5
of an hour. Darcy harvests corn at a constant rate.
\newline
How many acres does she harvest per hour?
\newline
acres per hour
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Charlie reads quickly. He reads
1
3
7
1 \frac{3}{7}
1
7
3
pages every
2
3
\frac{2}{3}
3
2
minutes. Charlie reads at a constant rate.
\newline
How many pages does he read per minute?
\newline
pages per minute
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Elizabeth is going to flip a fair coin
100
100
100
times.
\newline
What is the best prediction for the number of times that the coin will land tails up?
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
200
200
200
times
\newline
(B) Close to
200
200
200
times but probably not exactly
200
200
200
times
\newline
(C) Exactly
50
50
50
times
\newline
(D) Close to
50
50
50
times but probably not exactly
50
50
50
times
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Amit is going to guess on all
20
20
20
questions of his multiple-choice test. Each question on the test has
4
4
4
answer options, and only one is correct.
\newline
What is the best prediction for the number of questions that Amit will answer correctly?
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
5
5
5
questions
\newline
(B) Close to
5
5
5
questions but probably not exactly
5
5
5
questions
\newline
(C) Exactly
80
80
80
questions
\newline
(D) Close to
80
80
80
questions but probably not exactly
80
80
80
questions
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Sunny's garden has
9
9
9
tomato plants,
5
5
5
pepper plants,
3
3
3
squash plants, and
6
6
6
pumpkin plants.
\newline
Complete the ratio.
\newline
For every
3
3
3
tomato plants in Sunny's garden, there is
1
1
1
□
\square
□
.
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Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by
b
+
2
c
+
3
j
b+2 c+3 j
b
+
2
c
+
3
j
where
b
b
b
is the number of hours Ben spends chopping,
c
c
c
is the number of hours Cam spends chopping, and
j
j
j
is the number of hours Justin spends chopping.
\newline
How many trees do they chop down after Ben spends
8
8
8
hours chopping, Cam spends
3
3
3
hours chopping, and Justin spends
4
4
4
hours chopping?
\newline
trees
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