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Math Problems
Grade 7
Compare ratios: word problems
According to Jax's pedometer, he walked \\[\(2\).\(783\)\,\text{km}\\] while taking care of the livestock in the morning and \\[\(3\).\(124\)\,\text{km}\\] taking care of the livestock in the evening. How far did Jax walk while taking care of the livestock today?
\(\newline\)A) \(5\).\(907\) km\(\newline\)B) \(5\).\(907\) km\(\newline\)C) \(5\).\(907\) km\(\newline\)D) \(5\).\(907\) km
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Manny and his friend Vince go apple-picking every October. This year, Manny picked
4
4
4
pounds of red apples and
5
5
5
pounds of green apples. Vince picked
3
3
3
pounds of red apples and
6
6
6
pounds of green apples. Did Manny and Vince pick the same ratio of red apples to green apples?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Bernie owns the Bright Blooms flower shop. When he makes a small bouquet, he uses
3
3
3
roses and
6
6
6
lilies. When he makes a large bouquet, he uses
6
6
6
roses and
8
8
8
lilies. Does Bernie use the same ratio of roses to lilies in both bouquets?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Shawn and Robert are comparing the scout patches they've earned. Shawn has a total of
8
8
8
patches,
5
5
5
of which are explorer patches. Robert has a total of
6
6
6
patches,
3
3
3
of which are explorer patches. Do Shawn and Robert have the same ratio of explorer patches to total patches?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Last weekend, Erin went skiing at Snowy Peak Mountain. On Saturday, she skied
3
3
3
hard slopes and
4
4
4
easy slopes. On Sunday, she skied
4
4
4
hard slopes and
5
5
5
easy slopes. Did Erin ski the same ratio of hard slopes to easy slopes on both days?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Raymond and his friend Khalil each bought a stack of books from the bookfair. Raymond bought
1
1
1
graphic novel and
4
4
4
adventure novels. Khalil bought
2
2
2
graphic novels and
5
5
5
adventure novels. Did Raymond and Khalil buy the same ratio of graphic novels to adventure novels?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Jake is making bracelets to give to his sisters. He uses
4
4
4
rainbow charms and
8
8
8
white star charms for his younger sister's bracelet. He makes his older sister's bracelet a little bigger, so he uses
5
5
5
rainbow charms and
10
10
10
white star charms. Does Jake use the same ratio of rainbow charms to white star charms in both bracelets?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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In a class test consisting of
10
10
10
questions,
5
5
5
marks are awarded for every correct answer,
2
2
2
marks are deducted for every incorrect answer and no marks are given for questions not attempted. Mohan gets four correct and six incorrect answers. What is his total score?
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Venkat reached the station half an hour before the scheduled arrival of the train, the train was later by
1
:
30
1:30
1
:
30
hr and arrived at
6
:
20
6:20
6
:
20
hr. At what time venkat did reach the station ?
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In basketball, the number of points you score is given by
3
x
+
2
y
+
z
3x+2y+z
3
x
+
2
y
+
z
where
x
x
x
is three-pointers,
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
three-pointers,
5
5
5
two-pointers, and
6
6
6
free throws?
\newline
◻
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Albert is going to hire a makeup artist for a fashion show and is comparing prices. Bonnie charges
$
20
\$ 20
$20
as a booking fee and an additional
$
40
\$ 40
$40
per hour. Linda charges
$
45
\$ 45
$45
per hour, plus a booking fee of
$
10
\$ 10
$10
. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be?
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Kevin and Bao are making fruit salads for a picnic. Kevin mixes
3
3
3
cups of melon and
8
8
8
cups of apple and Bao mixes
1
1
1
cup of melon and
8
8
8
cups of apple. Whose fruit salad will taste more appley?
\newline
Kevin's fruit salad will be more appley.
\newline
Bao's fruit salad will be more appley.
\newline
The two fruit salads will be equally appley.
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In art class students are mixing black and white paint to make gray paint. Xochitl mixes
1
1
1
cup of black paint and
3
3
3
cups of white paint. Dominic mixes
4
4
4
cups of black paint and
3
3
3
cups of white paint. Whose gray paint will be lighter?
\newline
Xochitl's gray paint will be lighter.
\newline
Dominic's gray paint will be lighter.
\newline
The two gray paints will be equally light.
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In art class students are mixing blue and red paint to make purple paint. Gavin mixes
1
1
1
cup of blue paint and
2
2
2
cups of red paint. Zoey mixes
1
1
1
cup of blue paint and
5
5
5
cups of red paint. Whose purple paint will be redder?
\newline
Gavin's purple paint will be redder.
\newline
Zoey's purple paint will be redder.
\newline
The two purple paints will be equally red.
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In art class students are mixing blue and red paint to make purple paint. Brooklyn mixes
6
6
6
cups of blue paint and
5
5
5
cups of red paint. Jose mixes
6
6
6
cups of blue paint and
1
1
1
cup of red paint. Whose purple paint will be redder?
\newline
Brooklyn's purple paint will be redder.
\newline
Jose's purple paint will be redder.
\newline
The two purple paints will be equally red.
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In art class students are mixing black and white paint to make gray paint. Layla mixes
2
2
2
cups of black paint and
3
3
3
cups of white paint. Kiran mixes
4
4
4
cups of black paint and
3
3
3
cups of white paint. Whose gray paint will be lighter?
\newline
Layla's gray paint will be lighter.
\newline
Kiran's gray paint will be lighter.
\newline
The two gray paints will be equally light.
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Carlos and Alexandra are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Carlos mixes
4
4
4
cups of dough with
5
5
5
quarter-cups of chocolate chips and Alexandra mixes
4
4
4
cups of dough with
1
1
1
quarter-cup of chocolate chips. Whose cookies will be doughier?
\newline
Carlos's cookies will be doughier.
\newline
Alexandra's cookies will be doughier.
\newline
The two sets of cookies will be equally doughy.
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Students are making lemonade from a powdered lemon drink mix. Aaron mixes
5
5
5
cups of water and
3
3
3
teaspoons of powdered lemon mix. Idil mixes
5
5
5
cups of water and
4
4
4
teaspoons of powdered lemon mix. Whose mix will be more watery?
\newline
Aaron's mix will be more watery.
\newline
Idil's mix will be more watery.
\newline
The two mixes will be equally watery.
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There are
9
9
9
athletes at a track meet. How many different ways can they finish first, second, and third?
\newline
Answer:
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Jude factored
28
x
2
28x^{2}
28
x
2
as
(
14
x
)
(
2
x
2
)
.
(14x)(2x^{2}).
(
14
x
)
(
2
x
2
)
.
\newline
Yasmin factored
28
x
2
28x^{2}
28
x
2
as
(
7
x
)
(
4
x
)
.
(7x)(4x).
(
7
x
)
(
4
x
)
.
\newline
Which of them factored
28
x
2
28x^{2}
28
x
2
correctly?
\newline
Choose
1
1
1
answer:
\newline
(A) Only Jude
\newline
(B) Only Yasmin
\newline
(C) Both Jude and Yasmin
\newline
(D) Neither Jude nor Yasmin
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in the west region of the us, the ratio of densely vegetated land to sparsely vegetated land is
11
:
18
11:18
11
:
18
in the central region of the us, the ratio is
3
:
1
3:1
3
:
1
what is the difference in percentage of densely vegetated land from the west region to the central region?
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