a) If the household used 800 units of electricity, calculate the amount paid by the household. b) If the…

Question

a) If the household used 800 units of electricity, calculate the amount paid by the household. b) If the household paid GH₵ 285, how many units of electricity did they use for the month?

ScanSolve AI Tutor · Accepted Answer

Here's the breakdown of the electricity bill calculation based on the provided tariff table. First, let's clarify the tariff rates from the table: 1st 50 units: The table shows "GHd10. ". Given the context of increasing rates per unit for subsequent blocks, it is assumed that this refers to GHC 0.10 per unit. If it were GHC 10.00 total for the first 50 units, the average rate (GHC 0.20/unit) would be higher than the next block's rate (GHC 0.15/unit), which is unusual for a tiered tariff system. Next 100 units: GHC 0.15 per unit Next 150 units: GHC 0.33 per unit Next 300 units: GHC 0.50 per unit (The OCR "Boo units" is interpreted as "300 units" from the image) Next 400 units: GHC 0.66 per unit a) If the household used 800 units of electricity, calculate the amount paid by the household. Step 1: Calculate the cost for each block of units consumed. Cost for the first 50 units: 50 units × GHC 0.10/unit = GHC 5.00; Units remaining: 800 − 50 = 750 units Cost for the next 100 units: 100 units × GHC 0.15/unit = GHC 15.00; Units remaining: 750 − 100 = 650 units Cost for the next 150 units: 150 units × GHC 0.33/unit = GHC 49.50; Units remaining: 650 − 150 = 500 units Cost for the next 300 units: 300 units × GHC 0.50/unit = GHC 150.00; Units remaining: 500 − 300 = 200 units Cost for the remaining 200 units (from the "next 400 units" block): 200 units × GHC 0.66/unit = GHC 132.00; Units remaining: 200 − 200 = 0 units Step 2: Sum the costs from all blocks to find the total amount paid. Total amount paid = GHC 5.00 + GHC 15.00 + GHC 49.50 + GHC 150.00 + GHC 132.00; Total amount paid = GHC 351.50 The household paid GHC 351.50. b) If the household paid GHC 295.00, how many units of electricity did they use for the month? Step 1: Calculate the cumulative cost for each full block until the total payment is exceeded. Cost for 1st 50 units: GHC 5.00. Cumulative units: 50. Cumulative cost: GHC 5.00. Remaining payment: GHC 295.00 − GHC 5.00 = GHC 290.00. Cost for next 100 units: GHC 15.00. Cumulative units: 50+100=150. Cumulative cost: GHC 5.00 + GHC 15.00 = GHC 20.00. Remaining payment: GHC 290.00 − GHC 15.00 = GHC 275.00. Cost for next 150 units: GHC 49.50. Cumulative units: 150+150=300. Cumulative cost: GHC 20.00 + GHC 49.50 = GHC 69.50. Remaining payment: GHC 275.00 − GHC 49.50 = GHC 225.50. Cost for next 300 units: GHC 150.00. Cumulative units: 300+300=600. Cumulative cost: GHC 69.50 + GHC 150.00 = GHC 219.50. Remaining payment: GHC 225.50 − GHC 150.00 = GHC 75.50. Step 2: Determine the units from the next block using the remaining payment. The remaining payment of GHC 75.50 falls into the "next 400 units" block, which is charged at GHC 0.66 per unit. Units from this block = Remaining paymentRate for this block = GHC 75.50GHC 0.66/unit Units from this block ≈ 114.3939 units Step 3: Calculate the total units used. Total units used = 600 units + 114.3939 units Total units used ≈ 714.39 units The household used approximately 714.39 units.

A) If the household used 800 units of electricity, calculate the amount paid by the household. b) If the household paid GH₵ 285, how many units of electricity did they use for the month?

Answers

Step-by-step solution

Part a· 2 steps

Calculate the cost for each block of units consumed.

Sum the costs from all blocks to find the total amount paid.

Part b· 3 steps
$714.39 \text{ units}$

Calculate the cumulative cost for each full block until the total payment is exceeded.

Determine the units from the next block using the remaining payment.

Calculate the total units used.

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