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Math Problems
Grade 7
GCF and LCM: word problems
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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