Consumer arithmetic
Clement Radcliffe, Contributor

These boys from Cumberland High School cool out as they await a bus in Portmore, St. Catherine, recently. - Anthony Minott/Freelance Photographer

Let us begin by checking the answers to last week's practice exercise.

1. Calculate the value of 4 1/2 x 2/3 - 1/4

Solution

4 1/2 x 2/3 - 1/4.

The first step, of course, is to evaluate the product.

ie. 4 1/2 x 2/3 = 9/2 x 2/3 = 3.

Completing, 3 - 1/4 = 2 2/3 or 11/4

3. Simplify [2 1/3 - 1 5/8] ÷ 1 1/3

Solution

Using the order indicated by BOMDAS, we evaluate within the brackets:

2 1/3 -1 5/8 = 7/3 - 13/8

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

= 17/24

Dividing next, 1724 ÷ 1 1/3

= 17/24 x 3/4 = 17/32

4. Find the value of: 18.75 - (2.11)² (No. 1 (a) (ii), CXC January 2006)

Solution

18.75 - (2.11)²

= 18.75 - (2.11 x 2.11)

= 18.75 - 4.4521 = 14.2979

Solution

Using the order indicated by BOMDAS, we first evaluate the numerator.

2 1/4 x 4/5 = 9/4 x 4/5 = 9/5

Evaluating the denominator: 3/5 - 1/2 (The LCM of 5 and 2 is 10)

Dividing, 9/5 ÷ 1/10

= 9/5 x 10/1 = 9 x 2 = 18.

NB: The line in the question represents brackets and so the denominator could have been first evaluated.

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

ie. 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 = .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 40% of $800.

Solution

40/100 x $800 = $320.

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

Example 2

Schools were offered a 15% discount on the purchase of football gear. If a set of gear is valued at $180,000, how much less was paid?

Solution

15% of $180,000

= 15/100 x $180,000 = $27,000.

ie. The school paid $27,000.00 less.

NB: The amount the school paid is found as follows:

85/100 x $180,000 = $153,000.

The next situation is:

(B) Finding percentages, given the values.

Example 1

Express 3 m. as a percentage of 8 m.

(a) 30%
(b) 37.5%
(c) 62.5%
(d) 130%

Solution

3/8 x 100 = 37.5%

ie. 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 ... the loss = $500

The percentage loss

ie. 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%.

ie. 100% represents 100/30 x 69 = 230

ie. 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.

ie. The amount paid is $6,300 + $945 = $7,245

NB: As the amount represents 115%, you could also have found it as follows:

115/100 x $6,300 = $7,245.

In summarising, the following points should be noted:

• Percentage is a fraction of 100.
• The whole is represented 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 )%

Homework

Now for your homework.

1. Mr. Williams bought a plot of land for $40 000. The value of the land appreciated by 7% each year. Calculate the value of the land after one year.

2. In a certain country, electricity charges are calculated based on the following table:

Fixed charge Charge per kwH used

(i) Calculate the electricity charges for a customer who used 1003 kwH.

There is a government tax of 15% on the electricity charges.

(ii) Calculate the tax on the customer's electricity charges, giving your answer to the nearest cent.

(iii) Calculate the total amount paid by the customer.

(CXC January 2001,1b)

Clement Radcliffe is the principal of Glenmuir High School in May Pen.