The gas rate of every month of a certain gas company is the sum total of the fixed amount of basic charge and the charge corresponding to the amount of the gas used.
The charge corresponding to the amount used is calculated from the unit price per m3 provided in stages corresponding to the amount used.
The unit price is as follows.
The amount used Up to 10 m3 160 yen per 1 m3
Over 10 m3 up to 30 m3 X yen per 1m3
Over 30 m3 240 yen per 1 m3
In addition, the gas rate is calculated by 1 m3 increments.
For example, when it is used 40 m3, the charge is calculated as (basic charge) + 10 × 160 yen + 20 × X yen + 10 × 240 yen.
At Taro’s house, 28 m3 gas was used in October and the charge was 6,310 yen.
Moreover, 40 m3 gas was used in December and the charge was 9,150 yen.
Answer the following questions.
(1) Find the basic charge of gas and the unit price of X yen of a secondary stage.
(2) As for Taro’s house, the least amount of the gas used in a year is in August and the most is in February.
In February the amount of gas used was exactly 3 times in August.
Moreover, the gas rate in February also became exactly 3 times in August.
Find the amount of gas used and the gas rate in February.
The charge corresponding to the amount used is calculated from the unit price per m3 provided in stages corresponding to the amount used.
The unit price is as follows.
The amount used Up to 10 m3 160 yen per 1 m3
Over 10 m3 up to 30 m3 X yen per 1m3
Over 30 m3 240 yen per 1 m3
In addition, the gas rate is calculated by 1 m3 increments.
For example, when it is used 40 m3, the charge is calculated as (basic charge) + 10 × 160 yen + 20 × X yen + 10 × 240 yen.
At Taro’s house, 28 m3 gas was used in October and the charge was 6,310 yen.
Moreover, 40 m3 gas was used in December and the charge was 9,150 yen.
Answer the following questions.
(1) Find the basic charge of gas and the unit price of X yen of a secondary stage.
(2) As for Taro’s house, the least amount of the gas used in a year is in August and the most is in February.
In February the amount of gas used was exactly 3 times in August.
Moreover, the gas rate in February also became exactly 3 times in August.
Find the amount of gas used and the gas rate in February.
Answer
(1) Basic charge = 750 yen,
unit price = 220 yen
(2) The amount of gas used = 45 m3,
(2) The amount of gas used = 45 m3,
the gas rate = 10350 yen
