Question 1210331: In a certain year, the consumption pattern of electricity charges in a town was as follows:
the cost of the first 30 units was $1.00 per unit;
the cost of the next 30 units was $7.00 per unit;
the cost of each additional unit was $5.00.
(a) If Amaka used 420 units of electricity in January that year, calculate the amount paid.
(b) If Amaka paid $2,740.00 in the month of February, calculate the number of units
of electricity consumed.
(c) Find, correct to two decimal places, the percentage change in units of electricity
consumed by Amaka in January and February.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
The cost of the first 60 units of electricity is 30($1) + 30($7) = $240.
(a) Amaka used 420 units in January. That means 420-60 = 360 units at $5 each, for an additional cost of 360($5) = $1800. The total amount paid in January was $240 + $1800 = $2040.
(b) In February, Amaka paid $2740 for electricity. The first 60 units cost $240, so the amount paid at $5 per unit was $2740-$240 = $2500. That means $2500/$5 = 500 units at that rate, making a total of 60+500 = 560 units for February.
(c) Amaka paid $2040 in January and $2740 in February. The percentage change is
To two decimal places, that percentage change is 34.31.
ANSWERS:
(a) $2040
(b) 560 units
(c) 34.31%
Answer by ikleyn(52752)  (Show Source):
You can put this solution on YOUR website! .
In a certain year, the consumption pattern of electricity charges in a town was as follows:
the cost of the first 30 units was $1.00 per unit;
the cost of the next 30 units was $7.00 per unit;
the cost of each additional unit was $5.00.
(a) If Amaka used 420 units of electricity in January that year, calculate the amount paid.
(b) If Amaka paid $2,740.00 in the month of February, calculate the number of units
of electricity consumed.
(c) Find, correct to two decimal places, the percentage change in units of electricity
consumed by Amaka in January and February.
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In this problem, in part (c) they ask about the percentage change in units of electricity,
while @greenestamps calculated the percentage change in the cost.
So, a correct calculation for part (c) is
the percentage change in units of electricity =  =  =  = 33.33% (rounded). ANSWER
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The post solution note
How the question is posed in part (c), it makes the request ambiguous,
since from this form it is UNCLEAR, which of the two months is considered as the base for the comparison.
In this sense, the question is mathematically DEFECTIVE.
In my calculation, I took the January consumption of electricity as the base for the comparison.
Had I create this problem, I would formulate part (c) differently
(c) Find, correct to two decimal places, the percentage change in units
of electricity, consumed by Amaka, from January to February.
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