1971-08-30 — Page 14

FERSAC

ISRARY

育教僑華 頁第張四第2 日十初月七年亥辛圈复 WAH KIU YAT PO

郭日橋

30 AUC1971.

CITY HALL

●期星日十三月八年一七九一瑟公年十六市里堂中

♥育数、6.華

璀

業同學

暑期進修專欄

*(17) A shop bought milk at $9.60 per gallon and

sold it at 706; for each half-pint bottle. 199 bottles were sold in one day, how much profit did the shop make?

智慧出版社主编

EF 中學同學暑期進修專欄 書礙

NAME

CLASS

(17)

EXERETSE 13

MARKS DATE

英文數學

(E)

CHAPTER ELEVEN

SIMPLE PERCENTAGE

BRUSH-UP YOUR NODEAU MA

TICS (6).

Lecture 6

Abstract Oyatêms

An abstruct system consists of

1, "a.

n-void set of elements

set of relations between these elemente. One beselmust. a definition of equality, which provides a criterion for distinguishing one elemen from nother, and

a set of operations which are closed.

an operation which combines any two elementa or a Bys can to produce a single element of the Bystem is called a binary operation.

Samalerary operation maps each single anding (416ment

6lement of headde ser into ja

of the system.

set of los tu lates

ations which é assumed

cysten.

a set of N

postulat

a set of definition:

be valid for, the

A fire spatements or

"are deductions: from

which are agreementë

concerning teruindicay for conceale construpter

from the gelelon of the system.

Illustration: Let 2 Le

Es

The ayatem Bt of seta

eual is called a Boolean a

on E can be defined in terms of che

follows:- for all X, TEE

Examples

ICY 1FT ZUY =

Postulates:

(1) and are commutative.

(ii)

defined

A relation C operation U es

each of and. U is distributive: over the other. (iii) there exist distinct elements , and I în E

such that for all X¤ Ny

XUA QUÂ

A PERCENTAGE is alaply a ratio in which the second number is 100, 1 and normally represented by a fraction with denominator 300, Big 5 per sent written as 5% may denote the ratio 5 1:100 or may be reprinted. by the fraction

Exceple. 1

Express

la perce

20 20% 100%

Express (a) 0.375 as a percentage. SOLUTION

(b) 0.277

0.27

Example 3

Express. (a)

·SOLUTION

as a simple: (a) 35% -

man, whose salary is $8,000 a year, receives at inc

his new saldry, SOLUTION

The increase, in salary £2,000~ Therefore, the new annual salary his new salary is $9.00 per year,

ANSWER 1

Example S

If a teach

find. The

The iner

SOLUTION

case of 5

$400 a year 46.00

salary is raised from $500 per month to $120x

cade - perma

($12000 12 (800)

ANSWER: "Example 6

nortase per cent.

An article costing-1200 was sold te pricci SOLUTION:

*(3) What is 60% of 2 ft. 6 in?

*(2) khas is 33% of 50 feet?

(1 Each month a man spends 87% of his pay and

aves $100, How much does he earn each month?

(4) It A is. 30 lighter than By by what percentage

B heavier than A7

2(5) What is

Expl

of 3 gallons b pints?

(C) that is 15% of 2 cut. 15 16,7.

(7) 4. had 40% more money than B. After A had given $150. B the had $100 more than As' How much had A originally?

*(9) Amanent $50,00 on buying eggs at 20,00 per

160. Some of the eggs were bad, and had to be thrown away. He sold the good ones at $3.00. dozen and made a profit of 20% on the whole.. How many bad eggs were there? in,

A shop pays 175.00 for a piel of rice, and.. the retail price is 20% more than the cost. If a man buys 15:catties of this rice from the shop, how much does he pay? ̧.

A(10) man, bought 100 books ar $4.00 each. He sold

half of von (af 55.00 each,120 of them at $4.50 and the rest at $3.25. What was the percentage gain?

article was bought by A and sold to a atlas pright of 20. sold it foc at a profit of 25

(6)

s

Cheza $300, how much did A. pay for it? ~ (11) * (12) A Day saved a certain sun of money. His fathe

increased it by 50%. If the total savings Famounted to $131.70, how much had his father

put in?

(13) Mr. Wong had 20 more money than Mr. Chan

After Mr. Hong had given Mr. Chan $20 they vere etch left with equal sums of money. Luch had Nr. Chan at first?

How

2(14) 2 cut. 76 lb. of riñe were bought at selv,

The total delivery change is $10. At what' price per db mast it be sold to make a profit of 2032

Ion set was bought, by X and Saldi te tu fat a profit of do, I sold it to: Z at loss of make

56 find the'sel

dad X pars

The required šifl price: The required selling price.

EZLRCISE 10

We paid 3/10

(15)

ANSWER:

Example

A radio costing $200 is sold for $140; find the loss per con SOLUTION: The loss $200 - $140 $60

ANSWER:

Example 8

Therefore, the loss percentage -

The required loss percentage is

is 12% heavier than B, D is 20% heavier than C by hoir much

cent is A heavier than C? SOLUTION

Let C bo 100%

120

$1.00% 120%

(12) 2hr, 10, man.. EXERCIST 11

€110.14

$240

$100

A group is defined to be a system ♬ = {0, •¦• having one closed operation" o and satisfying following.

üla o is associative:

02

ao(b

an entity.

a for all a€ G

for all

ent

е G such

03 each EG, has an inverse a such that

ANSWER

Example 9

Then Bibe

And, so A will be

Is 34.4% heavier than

san collects a rent of $400 per month for a flat he owns and paya $204 for rates every three month's. what percentage of the rent are the rates?"

SOLUTION

· ANSWER (

The rate for each month $204 3. sbb The required percentage. $68 + $400 x

(2)1106.7,est. 56 1 (5) 0.325

~(6) 0,625 (7) 0908

(08) 970

(13) 1:05

35.403.5

$70.60

34.80415

(14) 184 50"x 150 (15) 3100 ($3.201 (1618 males +106) x 0,25 7-5 miles

115

(a)

b

(a) 0.357

(b) 0.21452

by8

(19)-01025

(42) 1.35 in

70)-(-x: 280) ·$52-

$0.30 x 24) - $66.40 17

(17) 2 cheang 7 chura

a = e

Example of groups •

(a) The rational numbers with audition as operation (1) The non-zero rational numbers with multiplication

as operation.

(e) The integers with addition as the operation.

Thm, 1s If a,b,cEG, then aobie aọc Thm, 24 For a, beg, each equations aox = and you

b has a unique solution.

3: For every a, the inverse of the inverse of

Thm. 41 For

a, bely, (aob)-7

be a system {},

Example 10

The required percentage is 17

14 piculs of beans were bought at $1.30 per catty. The total delivery.

charge is $5.00. At what price per catty: must it-ba sol to make a profit of OLUTION:

ANSWER 1

Example:11

The total cost including delivery charge

$1.30

x 150 + $5.00 $195 + $5 - $200 The required selling price per catty

$200.x

+100 $2:46

100 The required selling price is $2.40

merchant bought 20 books at $3.20 each. We sold 30 of them a

$4.50 each; another 30 at $4.00 each and the remainder at $2. eugh." What was the percentage gain?

SOLUTION:

ANSWER:

NAME CLASS

Profit - Selling Price – Cast Price

= $4,50 x 30 + $4.00 × 39 + $2.50 x 10 - $3.20 x 70

$135 + $120 + $25 - $224 - $56,.

The required percentage gained - $56 + $224 × 100% = 25% The required percentage was 25%

EXERCISE 12

MARKS DATE

*(5) What is 33% of 2 weeks 2 days 3 hours?

6) In a certain place, if 42% are men, 28% are.. women, what percentage are children? If the population is 900,000, how many children are there?

A clerk, whose salary is $700 a month, receives an allowance of 5%. Find his, total income per year.

(5)

月100元度70$12,0005

RARE 12% Bl ** 20 JA

159某人有我一口,每月,

例10 英人食一期,每戶每1.3元,這費35元,若業獲利20%。間每片當價腰勺若千十

【例類11 某商人以年本3元2务之便贼70本,其中30本以国

C

康資田,其為以每本2元5角之地,問他軍利百分之愁?

練習十

茶女以传疑理46.5%際說 37.5%數鋼述,問她濫餘若干Y 化2.31為百分

(4)2.8县:2的百分之热?

15) 2星期2日3小時的33-6是多少

C67 某地42%儒加入,28%為女人,問孩子法百分之掑?若該啦!

(?) 茶文微的金儒每月100元,蕪得簿645%,問他每年收入爲若干? 2)從街125,000元購買生宇一昕*幫 22000元資出,求仍蝕之百分率

(D)「味一只守價為250元,若利25%,宅價。

(IO) ALBI BILOT15%, ORDE 20%% • BALDTET? (1)、某人扇去入的5%,只每年清720元,問他每年的投入需若干? (12) ASRDAUS BOB RE=201 RIBLE.

(13) 蒸(海本元之頭280本・中120本以民本元之資・120本以

H• #JEZESTZRRIN, MUTHBAZEN

(14) BANG,000 £ƒX £=] • 14,000%F3% Y A# • #XRTION, MYAN

NAIN DRAWIN

(5)相一順,設潋第223元,期的15%,若四年利15%,問登價康雪若干?:

(16) A TN1,800元駕入美代品,轉貸與日,達利23%,B轉變異C,若本23%。 閃C解入购

GAST?

《奖)、鮮制受機每加69元6角,言個每瓶7角,每瓶容量爲平品除,茶商店~

,閒置利若干?

(1) 24763†#180VES D7

辣智十三

Subgroups t

Any non-empty subset ý of is a subgroup of y

is itself a group with respect to o.

"Obviously {e} where e is the identity element of G.

A proper subgroup of the multiplicative group

G1 {1, −1, 1, -1} ±0 G = {1, -1}

Field

A field is defined

0 having 2 closed operat following:

and satisfying the

F.1 The system [F; Of is a commutative group with

identity denoted

F.2: The system {F, 0]

identity denoted by

F.3 The operation

0.18

tributive over

(1) If girl spent 46.5% of her money on books,

37.5% on buying pens, what percentage remained? +(2) Express 2.31 as a percentage.

(3) Express 1271% as a decimal.

*(4) Express 2.8 as a percentage of 2.

(8) Peter bought a nouse for $25000 and had to sell

-it for $22,000, find his loss per cent,

(8)

a commutative group with

(9) By selling a radio for $250, a man made a profit

of 25%, find the cost price,

C2

508493-%£697

3

(10) If A is 10% heavier than B, B is 15% heavier

than C, C is 20% heavier than D. By how much percentage is A heavier than D7

:(10)

・(11) David'

spent 75% of his income. Fina na income if he saved $720 a years (12) If the price of an article is raised by 105,

the increase in the price is $20 Find the new price...

(11).

(6) 294 165015750U?

(12)

4) AEBBƆ% • MBHAYET

2.2

(5) 36124966-197

(3) AMEMAHBOOK SAAB150TE, BILA SICUT ATASKAL

(13) A merchant bought 280, books at, $6.00 each,

He sold 120 of them at $9.00 another 120 at $8,00 each and the rest at $5.00 each, What was the percentage gain?

350

(13)

Ca is the additive inverse, while a is the multiplicative inverse or

Letic H x I, where is the set of

Equality, addition, and multiplica

defined as follows

(a,b) (c,d) irr

(a,b) ✪ (c,d) × (a

(a,b) o (c,d).

The system C,

e and b d in E

Of is a fie

nus

in C are

4 (14) A mân ănvests $6,000 in firm X and $14,000 in firm YXloses 10% and Y gains 10%, what sa the man's profit per cent

4(15) If a camera is sold for $228, there is a loss

of 5% Find 'how much must it be sold in order to gain 15?

̈4(16) A bought an article for $1,800 and sold it

B at a profit of: 20%, sold it to Cat

* How much did C pay?

(15) $

·(16) S

*響在順比成本20%,今某人在該店買此襬米15斤,間任付者

#25%, #c†3007% • B8) A

入

(12)心

得—頭,他的父親多50%,以增加其次 問之謂分他的款国“干”

(IS)主作何疑比湖 520%,王生付給陳先生20元後,則兩人所有之縣調泪形,間練兔

*765817105% #20 » MOLESTING

WAY HOW YEWAZ· 10% 若公付588元,高