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Math Problems
Grade 7
GCF and LCM: word problems
Abe is going to plant
54
54
54
oak trees and
27
27
27
pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
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The Zamboni is an ice resurfacer invented by Frank Zamboni in the year
_
_
_
\_\_\_
___
to clean and resurface the ice in skating rinks. A Zamboni takes
_
_
\_\_
__
minutes to resurface an Olympic-sized skating rink. What is the minimum number of Zambonis working together at the same rate that could resurface an Olympic-sized skating rink in
_
_
\_\_
__
minutes or less?
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question: Anton watched
movies
\text{movies}
movies
in
year
\text{year}
year
. If Michael watched
as many movies as Anton did in year
\text{as many movies as Anton did in} \ \text{year}
as many movies as Anton did in
year
, which of the following best approximates the number of movies Michael watched in
year
\text{year}
year
?
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Sue and Ann went to the amusement park. They bought the same number of ride tickets, but Sue bought them in packs of
9
9
9
, and Ann bought them in packs of
6
6
6
. What is the smallest possible number of tickets they each bought?
\newline
_
_
\_\_
__
tickets
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Bernard is planting
15
15
15
bushes and
18
18
18
trees in rows. If he wants all the rows to be exactly the same, with no plants left over, what is the greatest number of rows Bernard can plant?
\newline
_
_
_
_
\_\_\_\_
____
rows
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The yearbook editor wants each page of the Activities section of the yearbook to have the same combination of color photos and black-and-white photos. If there are
15
15
15
color photos and
20
20
20
black-and-white photos, all of which the editor wants to use, what is the greatest number of Activities pages the editor can create?
\newline
_____ pages
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At a school event, adults are seated in groups of exactly
6
6
6
and children are seated in groups of exactly
3
3
3
. If there are the same number of adults as children, what is the minimum number of adults attending?
\newline
_
_
_
_
_
_
\_\_\_\_\_\_
______
adults
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A club has
10
10
10
girls and
15
15
15
boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
\newline
_
_
_
_
\_\_\_\_
____
groups
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Bonnie is buying AA batteries and D batteries. The store sells AA batteries in packs of
4
4
4
and D batteries in packs of
2
2
2
. If Bonnie wishes to buy the same number of AA and D batteries, what is the smallest number of each battery type that she can buy?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
batteries
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Barbara is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has
12
12
12
stuffed cats and
16
16
16
stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Barbara can place her stuffed animals into?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
groups
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By coincidence, Luther's Obedience School trained the same number of dogs and cats last week. The school teaches dogs in groups of
10
10
10
and cats in groups of
5
5
5
. What is the smallest number of cats the school could have had?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
cats
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Evelyn's apartment complex and the Wayne Commons apartment complex have the same number of apartments. However, Evelyn's apartment complex is built in groups of
11
11
11
apartments, while the Wayne Commons apartment complex is built in clusters of
5
5
5
. What is the smallest number of apartments could each complex have?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
apartments
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A P.E. teacher needs to divide
16
16
16
male students and
8
8
8
female students into teams, each with the same combination of male students and female students and nobody left out. What is the greatest number of teams that can be formed?
\newline
_____ teams
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Jim and Mabel are studying a set of new words for Spanish class. Jim decides to break the set into lists of
7
7
7
words. Meanwhile, Mabel creates lists of
8
8
8
words. What is the smallest number of words there could be?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
words
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Carla buys strawberry gum in packs of
9
9
9
pieces and blueberry gum in packs of
5
5
5
pieces. If Carla wants to buy the same amount of each type of gum, what is the smallest number of pieces of each flavor that she must buy?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
pieces
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Mrs. Campbell, the science teacher, collected
8
8
8
sedimentary rocks and
12
12
12
metamorphic ones. Now she wants to create some identical kits for studying rocks, without having any rocks left over. What is the greatest number of kits she can create?
\newline
_____kits
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Bob is buying pens and pencils from the store. Pens come in packages of
2
2
2
, but pencils are sold in packages of
3
3
3
. If Bob wishes to purchase the same number of pens as pencils, what is the smallest number of pens that he can buy?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
pens
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Zachary's Stationery sells thank-you cards in packs of
10
10
10
and birthday cards in packages of
9
9
9
. Surprisingly, the store sold the same number of each type of card this month. What is the minimum number of each card type that the store must have sold?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
cards
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Over the next two days, Carroll Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of
11
11
11
. On the second day, the agency will interview clients in groups of
8
8
8
. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?
\newline
_
_
_
_
\_\_\_\_
____
clients
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While performing a piece of music, Gary strikes the cymbals every
10
10
10
beats and the triangle is every
6
6
6
beats. If he just struck both at the same time, how many beats will pass before he again strikes them at the same time?
\newline
_____ beats
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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