Grade Seven Problems
If you can finish these problems, you'll
be smarter than I am.
1)
Three ducks and two ducklings weigh 32 kg. Four ducks and three
ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh
the same. What is the weight of two ducks and one duckling?
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2)
It takes one man one day to dig a 2m x 2m x 2m hole. How long does
it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?
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3)
A farmer grows 252 kilograms of apples. He sells them to a grocer
who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses
the same number of 5 kg bags as 2kg bags, then how many bags did he use
in all?
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4)
A 800 seat multiplex is divided into 3 theatres. There are 270 seats
in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre
3. How many seats are in Theatre 2?
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5)
In 1969 the price of 5 kilograms of flour was $0.75. In 1970 the
price was increased 15 percent. In 1971, the 1970 price was decreased by
5 percent. What was the price of 5 kilograms of flour in 1971?
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6)
7)
Mary has $50.00. She goes to the mall and buys lipstick and then
she buys shampoo, which is half the price of the lipstick. She then spends
half of what she has left on a purse, leaving her with $15.00.
How much did the shampoo cost?
How much did the lipstick cost?
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8)
Stephanie had $40.00 savings. Her mother gave her another $30.00
and her grandmother gave her $10.00 to buy a pair of cleats. The pair of
cleats Stephanie wants costs $54.99. If Stephanie buys the cleats at a
no TAX sale, write an equation using a variable to describe the amount
of money that Stephanie will have to contribute from her savings.
Solve for the variable.
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9)
Air is pumped into a vacuum sealed picture below room at a rate
of 2 litres per minute. How many seconds does it take to fill the room
with air? Use the information given to find the volume of the room.
a = 3dm 1 mL = 1 cm^{3
} b = 3dm 1000 mL = 1L
c = 4dm 1000 cm^{2} = 1 dm = 1L
d = 5dm
e = (3a  1)dm
f = (1/2b)dm
g = (3/8a + 3/8b)dm
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10)
Given a rectangular prism...
if the sides of the rectangle A have the same ratio to each other
as the sides of rectangle B, then what is

(a) The surface area of the prism?

(b) The volume of the prism?
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11)
The trails in a park resemble the following diagram. Find the total
length of the trails, given that all the circles have the same area and
circle 2 is tangent to the midpoint of L.
r = 10m
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12)
13)
A rectangular chalk board is 3 times as long as it is wide. If it
were 3 metres shorter and 3 metres wider, it would be square. What are
the dimensions of the chalk board?
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14)
Three people share a car for a period of one year and the mean number
of kilometers travelled by each person is 152 per month. How many kilometers
will be travelled in one year?
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15)
A car dealer claims that by buying a new car Mike will pay 1/5 less
for gas then he pays for the car he currently drives. If the car Mike currently
drives costs 1/6 less to gas up than Dave's car, and Dave pays $700.00
per year, what will it cost Mike to put gas in a new car for one year (assuming
all cars will be travelling the same distance)?
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16)
A side of the equilateral triangle A is twice the length of a side
of triangle B.
How many triangle B will fit into triangle A?
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17)
A storage facility has space for 225  8 litre boxes and 515  27
litre boxes. What is the volume of the facility? What percent of the total
volume is filled by 150 of the 8 litre boxes and 5 of the 27 litre boxes?
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18)
Marvin's Taxi Service charges $0.30 for the first kilometre and
$0.05 for each additional km. If the cab fare was $3.20, how far did the
Taxi go?
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19)
Shawn started his car (automatic shift), drove 8km and spent 2 minutes
at a stop light. Rachel (driving a manual shift) started her car and drove
9km with no stops. Who used more gas?
Table of Gas Usage
Automatic Manual
IDLING .16 L/min .16 L/min
STARTING 0.05 L 0.05 L
MOVING 1L/22 km 1L/20 km
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20)
21)
The number of hours left in a day on Mars was 1/4 of the number
of hours that had already passed. How many hours were left in the day?
Day on Mars 40 hours.
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22)
A cereal company decided to increase the height of its boxes by
30 percent and reduce the width in order to maintain the same volume.
If initially, length = 20cm
height = 40cm
width = 30cm
What will the new height and width be if length stays the same?
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23)
Cars Barks
+
6  4
7  7
8  10
9  13
10  16
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24)
There are 360 degrees in a circle. If the population of various planets
are represented by a circle graph, match the percentage of the population
of the solar system that is found on each planet with an area on the graph.
Planet Percent
+
Earth  27.78%
Mars  20.80
Venus  16.67
Jupiter  2.78
Mercury  2.78
Neptune  6.11
Saturn  8.33
Uranus  13.06
Pluto  1.67
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25)
A tire shop that sells only one size of tire, .75 metres in diameter,
decides to sell tires for big rigs that are 1.5 metres in diameter. If
the cost of the .75 meter tires is $100.00 for four, how much will it cost
for the 18 tires required for a big rig? Prices increase proportionally
with size.
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26)
Four friends buy a pizza that costs $20.00. Each person contributes
a the following amount of money.
Jane $5.00
Mike 8.00
Mary 3.00
Joe 4.00
Each person will eat an amount of pizza proportional to the amount of
money they paid.
1)Draw a circle graph that represents the amount each eat.
2)Draw the circle graph if Mike only eats half of his pizza and gives
half of what he has left to Mary.
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27)
A boy ate 100 cookies in five days. Each day he ate 6 more than
the day before. How many cookies did he eat on the first day?
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28)
M and N are the midpoints of the sides of a square. What is the
ratio of the area of traingle AMN to the area of the complete square?
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29)
There are 6 short pieces of link chain, each having 4 links. It
takes 10 seconds to cut a link and 25 seconds to weld it back together.
What is the shortest possible time to make the longest chain?
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30)
31)
An artist draws a picture of a house with a rose bush in front.
In his picture the rose bush is 1.5cm high and the house is 7.5cm high.
In reality the rose bush is .75 metres high. How tall is the house (in
metres)?
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32)
This picture shows a triangle in which 3 lines are drawn to one or
the other of the opposing sides from each of two vertices. This divides
the triangle into 16 nonoverlapping sections.
If 4 lines are drawn in the same way, how many nonoverlapping sections
will the triangle have?
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33)
The sports commentator on the CFXU radio station summarized the
points scored by the St. F. X. Basketball Team during this season as follows:
"The SMU scored a total of 1729 points in the last season. This year
St. F. X. scored of 1653 points. ST. F.X. received 38 percent of the points
for the total season of all 4 teams. SMU finished in second place. Acadia
received only 14 percent of the points and was beaten for third place by
Dalhousie by 50 points."
If there were only 4 teams in the season, how many points did each
team receive?
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34)
The midpoints of the sides of a quadrilateral are joined. What fraction
of the quadrilateral is shaded?
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35)
Rachel and Stephanie earn $5.15/hour. Rachel works 13 hours each
week and Stephanie works 20 hours per week. Stephanie does not get any
paid vacation time. How long a vacation would Stephanie have to take to
make the same amount of money as Rachel in one year?
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36)
The Town of Antigonish has decided to put a paved path around Columbus
Field. The path will be built so that the area of the park remains the
same. If the path is to be 3m wide...
a) What will be the perimeter of the path and the park? The dimensions
of the park are 210m x 460m.
b) What will be the area of the paved portion of the park?
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37)
Bacteria in a petri dish double the area they cover every day. If
the dish is covered after 16 days, on what day was only one quarter of
it covered?
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38)
Joe buys a cup of coffee that costs $1.08. He pays with a two dollar
coin.
If the cashier gives him 8 coins for his change, what could these
coins be?
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39)
Write the linear equations that describe the diagonals of this trapezoid.
What is one property of these diagonals?
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40)
Water conservation can be a big problem in some parts of the world.
If a community's water pump drips 3 drops every second and each drop is
1 1/3ml, how much water will be wasted in one year?
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41)
Square ABCD has the centers of 4 equal circles as its vertices.
Find the shaded area.
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42)
43)
Points A and B on a map are 12km apart if you follow the path. A
troop of boyscouts leaves point A at 11:00 a.m.. They are all carrying
packs and travel 3km/hr until they reach point C at 12:45. If they want
to reach point B by 2:00, how fast will they have to go?
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44)
Regular pentagon ABCDE is enclosed in a circle. If the radius of
the circle is 5 and each side AB = BC = CD = DE = EA = 5.88, find the area
of the pentagon.
(In a 90 degree triangle, using pythagorean theorem c = square root
of a^{2} + b^{2})
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45)
Line AB is parallel to line CD
The semicircle AED has diameter AD of 6cm. What is the area of the
trapezoid ABCD plus the semicircle AED?
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46)
In the quadrilateral ABCD, angle A is 120 degrees, angle D is two
thirds of angle C, and angle B is 90 degrees. Find angle C.
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47)
Find the area of quadrilateral EFGH.
Given (HC)^{2} + (CG)^{2} = (HG)^{2}
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48)
Two gear wheels A and B are in contact. One wheel (A) has 36 teeth.
The other (B) has 24 teeth. How many times must the smaller wheel turn
before the larger wheel completes a revolution?
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49)
Two trees of height 20m and 30m have ropes running from the
top of each tree to the bottom of the other tree. How high above the ground
do the ropes intersect?
The trees are 40m apart.
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