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Lecture notes Business mathematics (BMD115D) $5.50   Add to cart

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Lecture notes Business mathematics (BMD115D)

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Notes and in depth explanation of how to deal with FORMULAS

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  • August 24, 2024
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  • 2024/2025
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CHAPTER 9

FORMULAS

AIM: To find the value of a formula using substitution.
To change the subject of a formula, using the inverse operations.
To change the subject of a formula and calculate the value of the new subject.

9.1 SUBSTITUTION

One uses a recipe to bake a cake. A formula is like a recipe, guiding you to reach a certain result.

l

A b


The area of a rectangle is given by the formula A = l x b where

A = area
l = length of rectangle
b = width of rectangle.

A, l and b act like variables (unknowns). They can vary from situation to situation.

EXAMPLE 9.1

A person wants to paint his verandah. The length of the verandah is 7 metre and the width 3
metre. What is the total area he wants to paint?

We know the area of a rectangle is given by A = l x b.

So we substitute l = 7 and b = 3 in the formula:
A = 7x3
A = 21 m²

EXAMPLE 9.2

Suppose his verandah was 5 metre long and 2 metre in width, what would the area be?

We use A = l x b and substitute l = 5 and b = 2.

Area = 5 x 2
Area = 10 m²

, 56

EXAMPLE 9.3

The number of beats of a person's pulse is described by the formula n = 90t
where n = number of beats and
t = time in minutes.

Calculate the number of times his pulse beats in:

9.3.1 10 min

n = 90t
Substitute t = 10 minutes:
n = 90(10)
n = 900 beats

9.3.2 2 hours

n = 90t
Substitute t = 2 x 60 minutes:
n = 90(120)
n = 10800 beats

EXAMPLE 9.4

d = 110t expresses the distance a car travels at a speed of 110 km/h.
(Distance = speed x time). Calculate the distance travelled in:

9.4.1 2 hours

Distance travelled for t = 2 hours:
d = 110(2)
d = 220 km

9.4.2 5½ hours

Distance travelled for t = 5½ hours:
d = 110(5,5)
d = 605 km

EXAMPLE 9.5

Find the value of (a + b)(b + c) if a = 2, b = 3 and c = 4.

(a + b)(b + c) = (2 + 3)(3 + 4)
= 5 x 7
= 35

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