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Practical Use of Numbers

Exchange Rates

This is a practical use of direct proportion.

Example 1: Given $1 = R6,5, change $10 into rands.

$10 = 6,5 x 10 = R65

Example 2: Change R28 into dollars.

	R 1 = $1/6,5
	R28 = 1/6,5 x 28 = $4,31 (to the nearest cent)

Rule: Work out what one unit is in the money you are changing. Then multiply by the amount you are changing.

Simple Interest (I)

This is a practical use of percentages. It is a way of working out the interest gained on an investment.

The formula for simple interest is:	I = PTR 100

where
P = Principal (amount of money invested)
T = Time (in years)
R = Rate of interest (%)

Example 1: R600 is invested for 8 years at 15 % simple interest. How much interest will it earn? How much will the amount be after 8 years?

P = 600
T = 8	I =	600 x 8 x 15 100
R = 15
	I =	R720
	Amount =	600 + 720 =	R1 320

Note: Questions on this topic can ask for I, P, T, or R.

Simply make the required term the subject of the formula and substitute in the values given.

Example 2: R6 000 was invested for 1 year and 6 months. If the simple interest gained was R1 000, what was the rate of interest?

P = 6 000

T = 1 yrs

R =

100 I

(making R the subject)

R = ?

I = 1 000

R =

100 x 1 000

6 000 x 1

= 11

Compound Interest

In this case, the interest gained is added on each year and the next year's interest worked out.

Example 1: Work out the compound interest on R900 invested for 3 years at 5 %.

1^st year x 900 = R45

2^nd year x 945 = R47,25

3^rd year x 992,25 = R49,61 (to nearest cent)

Total compound interest = 45 + 47,25 + 49,61 = R141,86

Example 2: Calculate the amount after 3 years.

Amount = 900 + 141,86 = R1 041,86

For a larger number of years, we use a shorter method.

Using the figures in this example:

The amount at the end of the first year = 105 % of 900 = 1,05 x 900

At the end of the second year = 105 % of the first year = 1,05 x 1,05 x 900

So each year we multiply by 105 % = 1,05

Final amount = (1,05)³ x 900 = R1 041,86

Note: This can be done on the calculator as follows:

1,05 (power button) 3 x 900
^

For 15 years, we simply change the power to 15.

(1,05)¹⁵ x 900 = R1 871,04 (nearest cent)

Speed

Speed is defined as the distance travelled in one unit of time.

Example 1: A car travels 150 km in two hours. What was its average speed?

	In 1 hour the car travels 150 ÷ 2 = 75 km
	Speed = 75 km/hr

The units of speed can be km/hr or m/s.

Note: Always use the units asked for in a question.

Example 2: A particle travels 30 000 cm in 0,5 mins. What is its speed in m/s?

30 000 cm =	300 m
0,5 mins =	30 s
Speed =	300/30 = 10 m/s

Formula for average speed (S)

S = D
T

Where S = Speed
D = Distance
T = Time

To use this formula two of the values are given. By changing the subject of the formula, we can calculate the third.

Example 3: A car travels at a speed of 80 km/hr for 2 hours. What distance did it travel?

S = 80
T = 2
D = S x T (making D the subject)
D = 80 x 2 = 160 km

Example 4: A car travels 300 km at a speed of 60 km/hr. How long did it take?


S =	60
D =	300
T =	D
	S (making T the subject)
T =	300 = 5 hours
	60

Density

Density is the mass per unit volume.

Formula for density (D)

D =	M
	V

Where M = Mass (g)
V = Volume (cm³)

Example 1: The mass of a solid is 500 g and the volume is 1 000 cm³. Calculate the density.

M = 500
V = 1 000
D = 500 = 0,5 g/cm³ 1 000

Example 2: V = 3 000cm³, D = 0,2 g/cm³, so M = ?

M = D x V (making M the subject)
M = 0,2 x 3 000 = 600g

Triangle Method

Both types of problems relating to speed and density can be solved by using a triangle. This is known as the Triangle Method for Speed and Density.

Speed

The vertical line in the triangle means multiply and the horizontal line means divide.

So if two of the values of D, T or S are known, then you can work out the other using one of the following:

D/T = S

D/S = T

S x T = D

Density

The triangle for density is used in the same way.

M/D = V

M/V = D

D x V = M