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Math Problems
Grade 7
GCF and LCM: word problems
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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