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Math Problems
Grade 6
GCF and LCM: word problems
A
300
300
300
-acre farm produced
20
,
000
20,000
20
,
000
bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least
49
,
100
49,100
49
,
100
bushels of corn?
\newline
◻
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Increases in elevation are recorded with positive numbers. Decreases in elevation are recorded with negative numbers.
\newline
A group of hikers is hiking down a mountain. After
4
4
4
hours they descended
600
600
600
meters. They descended the mountain at the same rate each hour.
\newline
What was the hiking group's change in elevation each hour?
\newline
____meters
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A town uses positive numbers to track increases in population and negative numbers to track decreases in population.
\newline
The population has decreased by
300
300
300
residents over the past
5
5
5
years. The same number of residents left each year.
\newline
What was the change in the town's population each year?
\newline
residents
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Amy records deposits as positive numbers and withdrawals as negative numbers in her bank book.
\newline
Amy loaned an equal amount of money to each of
5
5
5
people. She loaned a total of
$
100
\$ 100
$100
. She recorded each loan by writing each amount in her bank book.
\newline
What is the amount Amy recorded in her bank book for each loan?
\newline
$
\$
$
____
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An elementary school in Birmingham has
8
8
8
classes participating in field day. Each class has
24
24
24
students. The students are placed on teams of
6
6
6
to compete in each activity.
\newline
What is the minimum number of teams needed for every student to participate?
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To rent a car for one week, a car rental company charges a
$
200
\$ 200
$200
base price as well as
$
0.45
\$ 0.45
$0.45
per mile. Jennifer will rent a vehicle at this company, but she has a
$
275
\$ 275
$275
budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?
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Moussa and Nicole are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Moussa mixes
4
4
4
cups of dough with
1
1
1
quarter-cup of chocolate chips and Nicole mixes
6
6
6
cups of dough with
1
1
1
quarter-cup of chocolate chips. Whose cookies will be more chocolaty?
\newline
Moussa's cookies will be more chocolaty.
\newline
Nicole's cookies will be more chocolaty.
\newline
The two sets of cookies will be equally chocolaty.
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Wyatt wants to buy a car. The maximum loan he can get from the bank is
$
16
,
465
\$ 16,465
$16
,
465
. If Wyatt has
$
2
,
035
\$ 2,035
$2
,
035
available to make a down payment, what is the highest valued car he can purchase?
\newline
Answer:
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Sadie and her children went into a grocery store where they sell peaches for
$
1.25
\$ 1.25
$1.25
each and mangos for
$
0.50
\$ 0.50
$0.50
each. Sadie has
$
9.50
\$ 9.50
$9.50
to spend and must buy no less than
13
13
13
peaches and mangos altogether. If Sadie decided to buy
4
4
4
mangos, determine all possible values for the number of peaches that she could buy.
\newline
Answer:
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Lauren has some nickels and some dimes. She has no more than
21
21
21
coins worth no less than
$
1.35
\$ 1.35
$1.35
combined. If Lauren has
10
10
10
dimes, determine the minimum number of nickels that she could have.
\newline
Answer:
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Fawzia and her children went into a restaurant where they sell hamburgers for
$
6.50
\$ 6.50
$6.50
each and tacos for
$
4
\$ 4
$4
each. Fawzia has
$
80
\$ 80
$80
to spend and must buy a minimum of
15
15
15
hamburgers and tacos altogether. If Fawzia decided to buy
10
10
10
tacos, determine the maximum number of hamburgers that she could buy.
\newline
Answer:
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A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and
150
y
d
150 \mathrm{yd}
150
yd
of fencing is available, find the largest total area that can be enclosed.
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Francine uses
2
3
\frac{2}{3}
3
2
cup of pineapple juice for every
1
3
\frac{1}{3}
3
1
cup of orange juice to make a smoothie.
\newline
Enter the number of cups of pineapple juice Francine uses for
1
1
1
cup of orange juice.
\newline
□
\square
□
cups of pineapple juice
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Ben drinks tea at an incredible rate. He drinks
3
1
2
3 \frac{1}{2}
3
2
1
liters of tea every
2
3
\frac{2}{3}
3
2
of an hour. Ben drinks tea at a constant rate.
\newline
How many liters of tea does he drink in one hour?
\newline
liters
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Jerry is a judge. He hears
5
5
5
cases every
2
3
8
2 \frac{3}{8}
2
8
3
hours. Jerry hears cases at a constant rate.
\newline
How many cases does he hear per hour?
\newline
cases per hour
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Uncle Drew scored
28
28
28
points in
5
5
6
5 \frac{5}{6}
5
6
5
minutes during a game of basketball.
\newline
How many points did he average per minute during that
5
5
6
5 \frac{5}{6}
5
6
5
minutes?
\newline
points per minute
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Brian irons
2
9
\frac{2}{9}
9
2
of his shirt in
3
3
5
3 \frac{3}{5}
3
5
3
minutes. Brian irons at a constant rate.
\newline
At this rate, how much of his shirt does he iron each minute?
\newline
of his shirt
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In basketball, the number of points you score is given by
3
x
+
2
y
+
1
z
3 x+2 y+1 z
3
x
+
2
y
+
1
z
where
x
x
x
is threepointers,
y
y
y
is two-pointers, and
z
z
z
is free throws (one-pointers).
\newline
What is the total number of points scored by a player who makes
3
3
3
three-pointers,
5
5
5
two-pointers, and
6
6
6
free throws?
\newline
points
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Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid
4
4
4
bones, Barry hid
5
5
5
bones, Larry hid
10
10
10
bones, and Goby hid
13
13
13
bones.
\newline
Find the mean number of dog bones.
\newline
dog bones
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Lupe's dogs love to hide bones. Bubba hid
5
5
5
bones, Barry hid
4
4
4
bones, Larry hid
13
13
13
bones, and Goby hid
10
10
10
bones.
\newline
Find the median number of bones. bones
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Heather is a cashier. She can ring up
12
12
12
customers in
9
9
9
minutes.
\newline
At this rate, how many minutes does it take her to ring up
4
4
4
customers?
\newline
minutes
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Teresa is maintaining a camp fire. She can keep the fire burning for
4
4
4
hours with
6
6
6
logs. She wants to know how many logs
(
y
)
(y)
(
y
)
she needs to keep the fire burning for
18
18
18
hours. She assumes all logs are the same.
\newline
How many logs does Teresa need to maintain the fire for
18
18
18
hours?
\newline
logs
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Some friends are planning to make a neighborhood garden. The total area available for the garden is
210
\mathbf{2 1 0}
210
square meters, and they want this to be
1
1
3
1 \frac{1}{3}
1
3
1
times the area of the plant beds in the garden.
\newline
What should the area of the plant beds be?
\newline
square meters
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Tomas was able to fill
6
2
3
6 \frac{2}{3}
6
3
2
equalsized buckets with a total of
33
1
3
33 \frac{1}{3}
33
3
1
liters of paint.
\newline
How much paint was in each whole bucket?
\newline
liters
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Ben likes to go in the covered dome when he feels overexcited. The dome covers an area of
1
2
3
1 \frac{2}{3}
1
3
2
square meters, which is
5
840
\frac{5}{840}
840
5
of the total area of the playground.
\newline
What is the total area of the playground?
\newline
square meters
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Paolo helped in the community garden for
2
3
4
2 \frac{3}{4}
2
4
3
hours this week. That was
1
5
6
1 \frac{5}{6}
1
6
5
equal-length shifts, because Paolo stopped early one day when it started to rain.
\newline
How long is a single shift?
\newline
hours
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Carlos has
4
5
\frac{4}{5}
5
4
of a tank of fuel in his car. He uses
1
10
\frac{1}{10}
10
1
of a tank per day.
\newline
How many days will his fuel last?
\newline
days
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An astronomer observes the velocity of a galaxy at a distance of
100
100
100
megaparsecs (
M
p
c
\mathrm{Mpc}
Mpc
) to calculate its distance two billion years from now using two different models. In the first model, the distance from the galaxy to Earth increases by
9
M
p
c
9 \mathrm{Mpc}
9
Mpc
every billion years. In the second model, the distance from the galaxy to Earth increases by
10
10
10
percent every billion years. Two billion years from now, how much further would the galaxy be in the second model compared to the first model in megaparsecs?
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In basketball, the number of points you score is given by
3
x
+
2
y
+
1
z
3 x+2 y+1 z
3
x
+
2
y
+
1
z
where
x
x
x
is threepointers,
y
y
y
is two-pointers, and
z
z
z
is free throws (one-pointers). What is the total number of points scored by a player who makes
3
3
3
threepointers,
5
5
5
two-pointers, and
6
6
6
free throws?
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Freddie's goal is to walk at least
25
25
25
kilometers a week. If he has already walked
13
13
13
.
6
6
6
kilometers this week, what is the minimum distance, in kilometers, he still needs to walk this week to meet his goal?
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The Silver Lake Reservoir in California is being drained to make way for an underwater pipeline. The reservoir holds
400
400
400
million gallons of water, and it is estimated that the drainage will take at least
25
25
25
days. If the water is drained at a constant rate, what is the maximum rate of drainage, in millions of gallons per day?
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3
x
+
2
y
≥
24
3 x+2 y \geq 24
3
x
+
2
y
≥
24
\newline
Erica's goal is to score at least
24
24
24
points in her next playground basketball game. The given inequality represents this goal, where
x
x
x
is the number of
3
3
3
-point field goals she scores and
y
y
y
is the number of
2
2
2
-point field goals she scores. If she scores
53
53
53
-point field goals, what is the minimum number of
2
2
2
-point field goals she must score to meet her scoring goal?
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Mindy and Troy combined ate
9
9
9
pieces of wedding cake. Mindy ate
3
3
3
pieces of cake and Troy had
1
4
\frac{1}{4}
4
1
of the total cake. How many pieces of cake were there in all?
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A
300
300
300
-acre farm produced
20
20
20
,
000
000
000
bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least
49
49
49
,
100
100
100
bushels of corn?
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Walter is trying to control his home energy costs. His bill consists of a monthly flat fee of
$
9
\$ 9
$9
plus
$
0.07
\$ 0.07
$0.07
per kilowatt hour of electricity used. If Walter does not want his electric bill to exceed
$
65
\$ 65
$65
per month, what is the maximum whole number of kilowatt hours he can use?
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The great snipe can fly up to
4
4
4
,
000
000
000
miles (
m
i
\mathrm{mi}
mi
) without stopping for food or water at a speed of
60
60
60
miles per hour (mph). What is the maximum number of days, to the nearest tenth, that the great snipe can fly without stopping?
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In the years from
2010
2010
2010
to
2015
2015
2015
, the basketball player LeBron James played
17
17
17
,
860
860
860
minutes, more than any other player in the National Basketball Association. Kevin Durant is second, with
15
15
15
,
595
595
595
minutes played in those years. If Kevin Durant averaged
38
38
38
minutes per game, what is the least number of additional games he would have had to play to surpass LeBron James's record? The answer should be a whole number.
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Michael is planning to join a local gym and is researching his options. His first option, Bodies In Motion, charges a one time enrollment fee of
$
60.00
\$ 60.00
$60.00
, plus an additional monthly fee of
$
18.00
\$ 18.00
$18.00
. His second option, Cardio World, does not have an enrollment fee, but charges
$
30.00
\$ 30.00
$30.00
per month. In how many months will the total cost for a gym membership at both gyms be equal?
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Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is
12
12
12
feet long, and each strand of his Christmas lights will wrap around a
70
70
70
-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?
\newline
A)
6
6
6
\newline
B)
7
7
7
\newline
C)
8
8
8
\newline
D)
9
9
9
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