Booklet 3 Problem Solving Level 6

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


7/17

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 '' '


10/17

'$ 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


12/17

(ns#er:

6()A =(DH@

start %. litres C %. %. litres C %.

moving 0km L

$' cm!C 1'


13/17

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


14/17

(ns#er:

@et , C the number of cookies eaten on the first day

Dookies Haten

ay 1 ,

$ , E 1


15/17

1'M L '!. C 32

(@8?6+H:

(cadia E . C 32 E . C 3.2

65?:

'!. -


16/17

(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

Documents

Booklet 3 Problem Solving Level 6