Booklet 3 Problem Solving Level 6
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Transcript of Booklet 3 Problem Solving Level 6
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8/10/2019 Booklet 3 Problem Solving Level 6
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Problem Solving
Booklet 3
This booklet provides opportunities for students to engage in activities that require
them to:
investigate;
make conjectures;
use problem-solving strategies;
apply their mathematical understanding;
verify solutions;
use mathematical language
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Problem Solving Questions - Booklet 3 Problems
1"
Three ducks and t#o ducklings #eigh !$ kg% &our ducks and three ducklings #eigh ''kg%
(ll ducks #eigh the same and all ducklings #eigh the same% )hat is the #eight of t#o
ducks and one duckling*
$"
+t takes one man one day to dig a $m , $m , $m hole% o# long does it take ! men #orking
at the same rate to dig a 'm , 'm , 'm hole*
!"
( farmer gro#s $.$ kilograms of apples% e sells them to a grocer #ho divides them into .
kilogram and $ kilogram bags% +f the grocer uses the same number of . kg bags as $kg bags/
then ho# many bags did he use in all*
'"
( 0 seat multiple, is divided into ! theatres% There are $7 seats in Theatre 1/ and there
are 1. more seats in Theatre $ than in Theatre !% o# many seats are in Theatre $*
."
+n 1232 the price of . kilograms of flour #as 4%7.% +n 127 the price #as increased 1.
percent% +n 1271/ the 127 price #as decreased by . percent% )hat #as the price of .
kilograms of flour in 1271*
3"
5ary has 4.%% 6he goes to the mall and buys lipstick and then she buys shampoo/ #hich
is half the price of the lipstick% 6he then spends half of #hat she has left on a purse/ leaving
her #ith 41.%%
o# much did the shampoo cost*
o# much did the lipstick cost*
7"
6tephanie had 4'% savings% er mother gave her another 4!% and her grandmothergave her 41% to buy a pair of cleats% The pair of cleats 6tephanie #ants costs 4.'%22% +f
6tephanie buys the cleats at a no T( sale/ #rite an equation using a variable to describe the
amount of money that 6tephanie #ill have to contribute from her savings%
6olve for the variable%
0"
The rent-a-stall horse barn has stalls for 1 horses% &orty percent of the stalls are for
ponies% 8n Tuesday/ there #ere $ ponies and a bunch of quarter horses at the horse barn%
The horse barn #as 7. percent full%
o# many quarter horses #ere in the stalls*
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2"
( rectangular chalk board is ! times as long as it is #ide% +f it #ere ! metres shorter and !
metres #ider/ it #ould be square% )hat are the dimensions of the chalk board*
1"
Three people share a car for a period of one year and the mean number of kilometerstravelled by each person is 1.$ per month% o# many kilometers #ill be travelled in one
year*
11"
( car dealer claims that by buying a ne# car 5ike #ill pay 19. less for gas then he pays for
the car he currently drives% +f the car 5ike currently drives costs 193 less to gas up than
aves car/ and ave pays 47% per year/ #hat #ill it cost 5ike to put gas in a ne# car
for one year as ?sage
(utomatic 5anual
+@+A> %13 @9min %13 @9min
6T(=T+A> %. @ %. @
58B+A> 1@9$$ km 1@9$ km
1."
The number of hours left in a day on 5ars #as 19' of the number of hours that had already
passed% o# many hours #ere left in the day*
ay on 5ars ' hours%
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13"
( cereal company decided to increase the height of its bo,es by ! percent and reduce the
#idth in order to maintain the same volume%
+f initially/ length C $cm
height C 'cm
#idth C !cm
)hat #ill the ne# height and #idth be if length stays the same*
17"
The number of times a dog barks depends on the number of cars passing%
o# many cars have passed #hen a dog barks $$ times* o# many barks for . cars*
Dars arks
------E-------
3 F '
7 F 7 0 F 1
2 F 1!
1 F 13
10"
( tire shop that sells only one siGe of tire/ %7. metres in diameter/ decides to sell tires for big
rigs that are 1%. metres in diameter% +f the cost of the %7. meter tires is 41% for four/ ho#
much #ill it cost for the 10 tires required for a big rig* Prices increase proportionally #ith
siGe%
12"
&our friends buy a piGGa that costs 4$%% Hach person contributes a the follo#ing amount
of money%
Iane 4.%
5ike 0%
5ary !%
Ioe '%
Hach person #ill eat an amount of piGGa proportional to the amount of money they paid%
1"ra# a circle graph that represents the amount each eat%
$"ra# the circle graph if 5ike only eats half of his piGGa and gives half of #hat he has leftto 5ary%
$"
( boy ate 1 cookies in five days% Hach day he ate 3 more than the day before% o# many
cookies did he eat on the first day*
$1"
(n artist dra#s a picture of a house #ith a rose bush in front% +n his picture the rose bush is
1%.cm high and the house is 7%.cm high% +n reality the rose bush is %7. metres high% o# tall
is the house
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$$"
The sports commentator on the D&? radio station summariGed the points scored by the 6t%
&% % asketball Team during this season as follo#s:
JThe 65? scored a total of 17$2 points in the last season% This year 6t% &% % scored of 13.!
points% 6T% &%% received !0 percent of the points for the total season of all ' teams% 65?
finished in second place% (cadia received only 1' percent of the points and #as beaten forthird place by alhousie by . points%J
+f there #ere only ' teams in the season/ ho# many points did each team receive*
$!"
=achel and 6tephanie earn 4.%1.9hour% =achel #orks 1! hours each #eek and 6tephanie
#orks $ hours per #eek% 6tephanie does not get any paid vacation time% o# long a
vacation #ould 6tephanie have to take to make the same amount of money as =achel in one
year*
$'"The To#n of (ntigonish has decided to put a paved path around Dolumbus &ield% The path
#ill be built so that the area of the park remains the same% +f the path is to be !m #ide%%%
a" )hat #ill be the perimeter of the path and the park* The dimensions of the park are $1m
, '3m%
b" )hat #ill be the area of the paved portion of the park*
$."
acteria in a petri dish double the area they cover every day% +f the dish is covered after 13
days/ on #hat day #as only one quarter of it covered*
$3"
Ioe buys a cup of coffee that costs 41%0% e pays #ith a t#o dollar coin%
+f the cashier gives him 0 coins for his change/ #hat could these coins be*
$7"
)ater conservation can be a big problem in some parts of the #orld% +f a communitys #ater
pump drips ! drops every second and each drop is 1 19!ml/ ho# much #ater #ill be #asted
in one year*
$0"
6ha#n bought a car for 4.3%% e sold it to =achel for .93 the price he paid for it% =achel
sold it to =aelene for 19. less than she paid% =aelene sold it to =ick for !9' #hat she paid%
)hat did =ick pay for the car*
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Problem Solving Questions Booklet 3 Hints
Kuestion 1
ints:
1" 6et up t#o equations
Kuestion $
ints:
1" &ind rate of one man
Kuestion !
ints:
1" @et , C total number of bags
Kuestion '
ints:
1" @et , C seats in Theatre !% Then number of seats in Theatre $ C , E 1. seats%
Kuestion .
ints:
1" @et 127 cost C
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Kuestion 1!
ints:
1" &ind distance travelled after first kilometer
Kuestion 1'
ints:
1" ?se table to calculate total amount of gas used by each person
Kuestion 1.
ints:
1" @et , C the number of hours that have already passed
Kuestion 13
ints:
1" (n increase in the height h by !M is
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Kuestion $'
ints:
1" ra# a sketch
Kuestion $.
ints:
1" )ork back#ards from day 13$" +f the amount covered doubles every day/ then each previous day is covered only half as much as
the ne,t day
Kuestion $3
ints:
1" There is more than one solution
Kuestion $7
ints:
1" @ook at ho# much #ater drips every second
$" Dalculate number of seconds in one year
Kuestion $0
ints:
1" Dalculate price each person paid for the car/ #orking from =achel to =aelene/ to =ick
Kuestion $2
ints:
1" istance C =ate L Time
$" =ate C istance9Time
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Problem Solving Questions Booklet 3 Answers
1"
(ns#er:
@et C the #eight of one duck
d C the #eight of one duckling
6olve:
OOOOOOOOOOOOOO
1 E d C 0 -----N C 0
6ubstitute to solve for d:
' E !d C '' '
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'$ E $, C 0
, C 12
+f there are , C 12 seats in theatre !/ then
Theatre $ has
1. E 12 C !' seats
."
(ns#er:
+f the price of . g of flour in 1232 C 4%7./ then
127 C 4%7. , 1%1. C 4%03$.
1271 C
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(ns#er:
7.M full C 7.M L 1 horses
C 7. horses
+f there are $ ponies/ there must be
C $%2
Total number of kilometers C 1 E
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(ns#er:
6()A =(DH@
start %. litres C %. %. litres C %.
moving 0km L
$' cm!C 1'
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Pattern:
13 - 1! C ! 1 - 7 C !
1 - 2 C 1 0 - 7 C 1
! barks for 1 car
Therefore/ $$ barks for 1$ cars%
10"
(ns#er:
@et , C price for each big rig tire
6iGe Price9tire
%7.m 419' C 4$.% each
1%.m ,
6olve for ,:
%7.m94$.% C 1%.9,
%7., C 1%. L 4$.%
%7., C 4!7%.
, C 4.%9tire
Therefore:
Price for 10 tires C 10
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(ns#er:
@et , C the number of cookies eaten on the first day
Dookies Haten
ay 1 ,
$ , E 1
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1'M L '!. C 32
(@8?6+H:
(cadia E . C 32 E . C 3.2
65?:
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(ns#er:
(mount of change Ioe receives:
4$% - 41%0 C 4%2$
T#o possible variations of coins received:
(ns#er:
Travel time from ( to D C 1$:'. -11: C 1 hr '. min C 1%7. hr
istance travelled:
C =ate L Time C ! km9hr L 1%7. hr
C .%$. km
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istance remaining