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Math Problems
Grade 7
GCF and LCM: word problems
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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Allie did push-ups every weekday this week. She did
8
8
8
push-ups on Monday,
14
14
14
push-ups on Tuesday,
18
18
18
push-ups on Wednesday,
6
6
6
push-ups on Thursday, and
8
8
8
push-ups on Friday.
\newline
Find the median number of push-ups.
\newline
push-ups
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Frances can complete
91
91
91
oil changes in
7
7
7
days.
\newline
How many oil changes can Frances complete in
11
11
11
days?
\newline
oil changes
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Kwesi is putting on sunscreen. He uses
3
m
l
3 \mathrm{ml}
3
ml
to cover
45
c
m
2
45 \mathrm{~cm}^{2}
45
cm
2
of his skin. He wants to know how many milliliters of sunscreen
(
g
)
(g)
(
g
)
he needs to cover
240
c
m
2
240 \mathrm{~cm}^{2}
240
cm
2
of his skin. He assumes the relationship between milliliters of sunscreen and area is proportional.
\newline
How many milliliters of sunscreen does Kwesi need to cover
240
c
m
2
240 \mathrm{~cm}^{2}
240
cm
2
of his skin?
\newline
m
l
\mathrm{ml}
ml
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Amira had
3
4
\frac{3}{4}
4
3
of a bag of cat food.
\newline
The food lasted
7
1
2
7 \frac{1}{2}
7
2
1
weeks.
\newline
How much cat food did Amira's cats eat per week?
\newline
bags
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After it snows, it takes Maria and her little sister Anita
1
2
\frac{1}{2}
2
1
of an hour to shovel the snow off of the sidewalks on their street. This is
2
3
\frac{2}{3}
3
2
of the time it takes Maria to do the same job by herself.
\newline
How long does it take Maria do this job by herself?
\newline
hours
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Katya is making a rectangular table that is
3
4
m
\frac{3}{4} \mathrm{~m}
4
3
m
wide. The table has an area of
1
1
5
m
2
1 \frac{1}{5} \mathrm{~m}^{2}
1
5
1
m
2
\newline
How long is the table?
\newline
m
\mathrm{m}
m
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Avi and Micah are teammates on a track and field team. Avi's best long jump is
1
1
6
1 \frac{1}{6}
1
6
1
times as long as Micah's. Avi's best long jump is
3
1
2
3 \frac{1}{2}
3
2
1
meters.
\newline
How long is Micah's best long jump?
\newline
meters
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Noam had a length of
13
1
3
c
m
13 \frac{1}{3} \mathrm{~cm}
13
3
1
cm
of ribbon and cut
3
1
3
3 \frac{1}{3}
3
3
1
equal-sized strips the full width of the ribbon.
\newline
How long is each whole strip?
\newline
c
m
\mathrm{cm}
cm
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Jun-seo notices that there are
13
13
13
right-handed players on his baseball team and
2
2
2
left-handed players.
\newline
What is the ratio of left-handed players to right-handed players?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
for every
13
13
13
\newline
(B)
2
2
2
for every
15
15
15
\newline
(C)
13
\mathbf{1 3}
13
for every
2
\mathbf{2}
2
\newline
(D)
15
\mathbf{1 5}
15
for every
2
2
2
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In a random sample of
250
250
250
frozen pepperoni pizzas of a particular brand,
7
7
7
do not have enough pepperoni slices. At this rate, how many of
12
12
12
,
000
000
000
frozen pepperoni pizzas of the same brand will not have enough pepperoni slices?
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Ben Frank is an electrician who installs lighting fixtures. He charges his clients
15
h
+
40
f
15 h+40 f
15
h
+
40
f
dollars, where
h
h
h
is the number of hours worked and
f
f
f
is the number of fixtures installed. What is the amount, in dollars, Ben Frank charges when he works
7
7
7
hours and installs
9
9
9
fixtures?
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A website offers digital movie rentals for
$
2.95
\$ 2.95
$2.95
per movie or a monthly subscription with unlimited movies for
$
12.95
\$ 12.95
$12.95
per month. If Zara is a monthly subscriber, what is the minimum number of movies she must watch each month to save money compared to renting each movie separately?
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Suraj and Dipti are playing minigolf. In minigolf, the player who completes the course with the fewest number of strokes wins. If Suraj finished the course in
72
72
72
strokes, and Dipti has
66
66
66
strokes before attempting the last hole, what is the greatest number of strokes Dipti can finish the last hole in and still win?
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A trivia contest asks both multiple choice and free response questions. Contestants receive
3
3
3
points for each correct multiple choice question and
5
5
5
points for each correct free response question, and they must score more than
60
60
60
points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes
x
x
x
, the number of multiple choice questions, and
y
y
y
, the number of free response questions, that she answered correctly?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
x
+
5
y
>
60
3 x+5 y>60
3
x
+
5
y
>
60
\newline
(B)
3
x
+
5
y
≥
60
3 x+5 y \geq 60
3
x
+
5
y
≥
60
\newline
(C)
3
x
+
5
y
<
60
3 x+5 y<60
3
x
+
5
y
<
60
\newline
(D)
3
x
+
5
y
≤
60
3 x+5 y \leq 60
3
x
+
5
y
≤
60
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A
(
x
)
=
−
1
4
(
x
−
25
)
2
+
625
A(x)=-\frac{1}{4}(x-25)^{2}+625
A
(
x
)
=
−
4
1
(
x
−
25
)
2
+
625
\newline
The area,
A
(
x
)
A(x)
A
(
x
)
, of a rectangular enclosure that can be made from a limited amount of fencing is shown, where
x
x
x
is the length of one of the sides of the enclosure, measured in feet. What is the maximum area that can be enclosed in square feet?
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The Zamboni is an ice resurfacer invented by Frank Zamboni in the year
1949
1949
1949
to clean and resurface the ice in skating rinks. A Zamboni takes
20
20
20
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 Olympicsized skating rink in
5
5
5
minutes or less?
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Paulo's economics course requires two papers-one long and one short-throughout the semester. The number of pages,
l
l
l
, in the long paper is
1
1
1
more than
2
2
2
times the number of pages,
s
s
s
, in the short paper. If the total number of pages for both papers is
40
40
40
, how many pages must be in the long paper?
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On January
1
st
,
2014
1^{\text {st }}, 2014
1
st
,
2014
, approximately
450
450
450
thousand buildings in the United States (US) had solar panels. This number increased by a total of about
180
180
180
thousand over the next
12
12
12
months. Assuming a constant rate of change, approximately how many months after January
1
st
,
2014
1^{\text {st }}, 2014
1
st
,
2014
would
900
900
900
thousand buildings in the US have solar panels?
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The Huffman Corporation would like to donate
15
15
15
computers and
20
20
20
printers to local schools. The corporation would like to make sure that each school receives the same set of computers and printers, with none left over. What is the greatest number of schools that The Huffman Corporation can donate to?
\newline
_
_
_
_
\_\_\_\_
____
schools
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