ELECTRICITY AND GAS PRICES FOR FAMILY USE, CHARGED BY ENERGY COMPANY




An energy company charged these prices in 2013.

Electricity price
23.15 cents per day
plus
13.5 cents for each unit used

Gas price
24.5 cents per day
plus
5.5 cents for each unit used


 (Mathematics Cambridge IGCSE Test 0580 s17 qp 41)


(a) i) In 90 days, the Siddique family used 1885 units of electricity.
Calculate the total cost, in dollars, of the electricity they used.

Answer:

90 days x 23.15 cents + 1885 units used  x 13.5 cents
= 27531 cents
= $275.31

So, $275.31 is the total cost of  Siddique family used the electricity, in dollar, in 90 days.

ii) In 90 days, the gas used by the Khan family cost $198.16 .
Calculate the number of units of gas used.

Answer:

Where m is the total number of units used by Khan family.
$198.16 = 90 days x 24.5 cents + m units used x 5.5 cents
$198.16 = 2205 + 5.5 m
19816 cents - 2205 = 5.5 m
17611 cents = 5.5 m
3202 units = m

So, Khan family used 3202 units in total in 90 days

(b) In 2013, the price for each unit of electricity was 13.5 cents.
Over the next 3 years, this price increased exponentially at a rate of 8% per year. Calculate the price for each unit of electricity after 3 years.

Answer:

This question is similar with compound interest question, because there is a word ‘increased exponentially’. So we have to use compound interest formula to calculate the answer.
The informations given are:
Principal (initial price/capital/investment) = 13.5 cents
Rate = 8% per year.
Time = 3 years.

Amount of price after 3 years is:
A = P (1+ R)^T
A = 13.5 (1+ 8/100)^3
A = 17 cents

(c) Over these 3 years, the price for each unit of gas increased from 5.5 cents to 7.7 cents.
(i) Calculate the percentage increase from 5.5 cents to 7.7 cents.

Answer:

Let say 5.5 cents as 100%  or initial value.

5.5 cents 100%
1 cents 100%  divided  by 5.5 = 18.18%
7.7 cents 7.7 x 18.18% = 140%

So, the percentage increase over 3 years is 140% - 100% = 40%

(ii) Over the 3 years, the 5.5 cents increased exponentially by the same percentage each year to 7.7 cents.
Calculate the percentage increase each year.

Answer:

Because it increased exponentially, we must use compound interest formula to calculate percentage increase from 5.5 cents to 7.7 cents for over 3 years.

Amount after 3 years = P(1+R/100)^3 years
7.7 cents = 5.5 cents(1+R/100)^3 years
7.7/5.5 = (1+R/100)^3
1.4 = (1+R/100)^3
Cuberoot(1.4) = 1+R/100
1.1187 = 1+R/100
0.1187 = R/100
11.87 = R

So, each year, the percentage increase is 11.87 percents.


(d) In 2015, the energy company divided its profits in the ratio

shareholders : bonuses : development = 5 : 2 : 6.

In 2015, its profits were $390 million.
Calculate the amount the company gave to shareholders.

Answer:

The ratio in the simplest form is 5 : 2 : 6.
The total parts of ratio are 13 parts, with 5 parts  are given to shareholders.

Let say $390 million as 13 parts or total value/parts.

13 parts $390 million
1 parts $390 million divided  by 13 parts = $30 million
5 parts $30 million x 5 parts = $150

So, shareholders will get $150 from the company



(e) The share price of the company in June 2015 was $258.25 .
This was an increase of 3.3% on the share price in May 2015.
Calculate the share price in May 2015.

Answer:
Let say $258.25  as 103.3%, because this price is already increase 3.3% compared to share price of previous month, May 2015.
And the share price in May 2015 as 100%.

103.3%   $258.25  
1% $258.25 divided  by 103.3  = $2.5
100% $2.5 x 100 = $250
So, in May 2015 the price of share was $250


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