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