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Consumer
arithmetic
Clement Radcliffe,Contributor
Let
us begin by checking the answers to
last week's Practice Exercise.
1.
Solution
Calculate the value of 51⁄2
x 2⁄3
- 1⁄4
51⁄2
x 2⁄3
- 1⁄4
The
first step, of course, is to evaluate
the product according to BOMDAS.
...
51⁄2 x
2⁄3 =
11⁄2 x
2⁄3 =
11⁄3
Completing,
11⁄3
- 1⁄4
= 44⁄12
- 3⁄12
=
41⁄12
2.
Simplify (31⁄3
- 15⁄8)
/ 11⁄3
Solution
Using
the order indicated by BOMDAS, we
evaluate within the brackets:
31⁄3
- 15⁄8
= 10⁄3
- 13⁄8 (L.C.M. of
3 and 8 is 24)
=
( (8 x 10) - (3 x 13) )/24 = ( 80
- 39 )/24 = 41⁄24
Dividing
next, 41⁄24
/ 11⁄3
= 41⁄24
x 3⁄4
= 41⁄32
3.
Find the value of: 35.75 - (2.34)3
Solution
35.75
- (2.34)3 = 35.75 - (2.34 x 2.34 x
2.34) = 35.75 - 12.813 = 22.937
Calculating
the value of: ( (41⁄3
- 15⁄6)
/ 21⁄2
x 22⁄3)
Solution
The
line represents brackets and so the
numerator may be evaluated first.
41⁄3
- 15⁄6
= 13⁄3
- 11⁄6
=
( (2 x 13) - (1 x 11) )/6
=
( 26 - 11 )/6 = 15⁄6
Evalutating
the denominator:
3⁄2
x 8⁄3
= 24⁄6
Dividing:
= 15⁄6
/ 24⁄6
= 15⁄6
x 6⁄24
= 5⁄8
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 as 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.
Therefore,
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 the 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%
...
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 = Loss/Cost price
x 100
=
500⁄2500
x 100 = 20%
... 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%
... 100% represents 100⁄30
x 69 = 230
...
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
...
The amount paid is $6, 300 + $945
- $7 245
N.B. 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 )%
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:
Fixed
charge
$3.50 |
Charge
per kwH used
15 cents |
(i)
Calculate the electricity charges
for a customer who used 1,200 kWh
There
is a government tax of 17.5% 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
Clement
Radcliffe is an independent contributor.
Send questions and comments to kerry-ann.hepburn@gleanerjm.com
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