Reviewing consumer arithmetic
Clement Radcliffe, Contributor

Students take notes during the mathematics session of the Youthlink/Caribbean Examination Council techniques seminar at the Montego Bay Civic Centre, St. James, on Monday, April 11. - Claudine Housen

LET US begin by checking the answers to last week's practice exercise.

1. Calculate the value of:
2 1/3 - 1 1/2, expressing your answer as a fraction.

Solution

2 1/3 - 1 1/2 = 7/3 - 3/2 = (14 - 9)/6 = 5/6 (L.C.M. of 3 and 2 is 6)

Answer is 5/6.

2. Find the value of (6 1/3 - 2 1/2 x 1/6)/2 + 1/2

Solution

Using the order indicated by BOMDAS, we first evaluate the numerator, beginning with the multiplication,

2 1/2 x 1/6 = 5/2 x 1/6 = 5/12

Completing the numerator: 6 1/3 - 5/12 = 19/3 - 5/12 = (76-5)/12 = 71/12

2 + 1/2 = 2 1/2 or 5/2

Dividing, (71/12)/(5/2) = 71/12 x 2/5 = 71/30

3. Calculate the value of: (2 1/3 - 1 5/8)/(1 1/3)

Evaluate within the brackets: 2 1/3 - 1 5/8 = 7/3 - 13/8 = (56-39)/24 = 17/24

L.C.M. of 3 and 8 is 24

Dividing next, (17/24)/(1 1/3) = 17/24 x 3/4 = 17/32

4. (16/25 x 5/7)/(8/25) = 16/25 x 5/7 x 25/8 = 10/7

The lesson today will continue with a review of selected areas of consumer arithmetic. Some popular topics are: cost price, selling price, discount, sales tax, hire purchase, simple and compound interest.

The concept of percentage is fundamental to these topics as our review will illustrate.

DEFINITION

Percentage is a fraction with its denominator being 100. Therefore, a% = a/100

It should be noted that a percentage may be expressed as a decimal fraction or as a vulgar fraction, for example, 25% = 25/100 = 1/4 = 0.25

I will illustrate by looking at three situations in which the problems may be presented:

A) Finding the value representing a certain percentage.

Example 1

Find 30% of $400

Solution: 30/100 x $400 = $120

This is the basis of finding values such as profit and loss, sales tax, general consumption tax, discounts, etc.

Example 2

Mrs. King bought a component set for $48,600. If a tax of 15% is payable, find the value of the tax.

Solution 15% of $48,600 = 15/100 x 48,600 = $7,290

Therefore, the tax is $7,290

Example 3

Schools were offered a 15% discount on the purchase of football gear. If a set of gear is valued at $80,000, how much less was paid?

Solution 15% of $80,000 = 15/100 x $80,000 = $12,000

Therefore, the school paid $12,000 less.

The next situation is:

(B) Finding percentages, given the values.

Example 1

Express 5m as a percentage of 8m.

a) 200%
b)40.0%
c) 62.5%
d) 130%

Solution 5/8 x 100 = 62.5%

Therefore, the answer is (c)

This is the basis of finding values such as percentage loss or gain, percentage tax, discount etc.

Example 2

A radio cassette, which cost $2,500, was sold for $2,000. Find the percentage loss.

Solution Profit = selling price - cost price = $2,000 - $2,500 =-$500

Therefore, the loss = $500

The percentage loss = loss/cost price x 100

500/2500 x 100 = 20%

Therefore, the percentage loss is 20%.

Please note that percentage gain and loss are calculated as a fraction of cost price. A common error is to use the selling price.

The third situation is:

C) Problems involving percentages.

Example 1

If 30% of a number is 69, then the number is:

(a) 90
b) 230
c) 189
d)139

Solution If 30% of a number is 69, then the number is equivalent to 100%. Therefore, 100% represents 100/30 x 69 = 230

Therefore, the answer is (b)

This is the basis of finding values such as cost price and selling price, hire purchase, etc.

Example 2

A set of tools is priced at $6,300 plus GCT (general consumption tax) of 15%. How much is actually paid for the tools?

Solution Cost Price is $6,300. Since the tax is 15%, then 15/100 x $6,300 = $945

Therefore, the amount paid is $6,300 + $945 = $7,245

In summarising, the following points should be noted:

* Percentage is a fraction of 100
* The whole is representated by 100%
* If the whole is increased by X%, then the value becomes (100 + x)%
* If the whole is reduced by x%, then the value becomes (100-x)%

Now, for your homework.

1. A discount of 20% is given on the cost of a pair of shoes, which was originally priced at $1000. What is the selling price of the shoes?

2. A company sells its printers to customers in order to make a profit of 25%. Calculate:

i) The price a customer pays for a printer which the company bought for $1,700.

ii) The price the company paid for a printer which was sold to a customer for $2,500.

(CXC June, 2000, 1c)

* Clement Radcliffe is principal of Glenmuir High School in Clarendon.