Mathematics Therapy

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From: Samuel Omoogah
Date: Thu, Sep 16, 2021, 11:03
Subject: LINEAR EQUATIONS AND INEQUALITIES
To:

Example 1:

Solve 1 3

------ - -------- =0

1-2x 24+x

Solution:

The common denominator of the two fractions is (1-2x)(24+x). Multiply each term by (1-2x)(24+x)

1×(1-2x)(24+x)-3×(1-2x)(24+x)

----------------------- ----------------------- =

(1-2x) (24+x)

0×(1-2x)(24+x

Divide by using(24+x) in the denominator to divide(24+x) of the numerator and (1-2x) of the denominator to divide that of the numerator.

The result will be

1×(24+x) - 3×(1-2x) = 0

Clear brackets

24 + x-3+6x= 0

Collect like terms

24-3 +x+6x=0

21+7x=0

7x= -21

Divide both side by 7

X = 3.

PERCENTAGE CHANGES
Percentage form a very good basis for comparing changes in the form of increase or decrease relative to the original values. Suppose commodity A increase I price from N500 to N800and commodity B increases in price from N 20 to N 35 within the same time. The increase in the original price of goods A and B are N 300 and N 15 respectively. This shows that A has increased far more in price than B.
This conclusion is faulty because we did not consider the original prices of the goods to know which one has increased more in price relatively to their original price.
To do this, we say :
Percentage increase in price of A = 300
--------- × 100%
500
= 60%

Percentage increase in price B = 15
----- × 100%
20
= 75%
This shows that the rate of increase is actually higher in B than in A . This is because for each N1. 00 in A , there is an increase of 60 Kobo but for each N 1.00 in B , there is an increase of 75 Kobo.
Example 1:
By what must a number be multiplied to
(a) increase it by 20% ( b) decrease it by 15% ?
SOLUTION
(a) The ratio of the new value to the old is 120: 100
Thus , the new value = 120
--------
100
times the old value.
= 6
---- or 1.2 times the old
5
value.

(b) The ratio of the new value to the old is 85 : 100
Thus , the new value = 85
------
100
times the old value.
or 17
---- or 8.5 times the old
20
value.

MORE EXAMPLES ON RATIO
Example 2:
Two brothers Peter and Paul were instructed by their parents to share a Pocket money of N400 in the ratio of 3 : 5 . How much does each receive?
SOLUTION
If we treat the part of the ratio as share :
Peter receives 3 shares while Paul receives 5 shares.
Total number of shares is 3+5=8
Amount in 8 shares = N400
Amount in 1 share = N 400
----------- =
8
N50
Amount in 3 shares = N50 × 3 = N 150
Amount in 5 shares = N50 × 5 = N250
Therefore , Peter receives N150 while Paul receives N250.

Example 3:
Partners Wole, Chima and Bako agreed to share profits (or losses) in the ratio of 4:3:6. Divide their profit of N78, 000 among them.
SOLUTION
The ratio 4:3:6 indicates that the profit will be shared into 4 + 3 + 6 = 13 shares. Wole will receive 4 of the 13 shares, Chima will receive 3 and Bako will receive 6 of the 13 shares.

Wole receives 4
--- of the profits =
13
4
--- × N78, 000
13
= N24, 000

Chima receives 3
--- of the profit =
13
3
----- × N78, 000 = N18, 000
13

Bako receives 6
--- of the profit =
13
6
---- × N 78, 000 = N36, 000
13