Petra’s electricity supply company charges her a fixed quarterly sum plus a rate per unit for electricity used. In the most expensive quarter last year (January to March), she used 2 000 units and her bill was $250. In the least expensive quarter (July to September), she used 600 units and her bill was $138. She is now adding extra insulation to her home which is expected to reduce her overall electricity consumption by 25%. What can she expect her January to March bill to be next year (if there are no increases in overall tariffs)? *

$210

Step-by-step explanation:

(January - March) charge last year :

Unit consumed = 2000

Bill = $250

(July - September) charge last year:

Unit consumed = 600 units

Bill = $138

Billing :

Fixed charge + rate per unit ;

Let fixed charge = c ; rate per unit = m

Billing can be represented by the equation :

mx + c = y

x = unit consumed ; y = total charge

Expensive quarter:

2000x + c = 250 - - - (1)

Least expensive quarter:

600x + c = 138 - - - (2)

From (2)

c = 138 - 600x ; plug into (1)

2000x + 138 - 600x = 250

1400x = 250 - 138

1400x = 112

x = 0.08

0.08 = x = rate per unit

From ; c = 138 - 600x

c = 138 - 600(0.08)

c = 90

Fixed charge = 90

Billing equation :

y = 0.08x + 90

If insulation will reduce unit consumption by 25%

Then, consumption in most expensive quarter will be :

(100 - 25)% * 2000

0.75 * 2000 = 1500 units

Charge will be :

(0.08*1500) + 90

= $210