Nancy and her family used 22,5 kl of water in March 2025 and were charged R371,80 (incl VAT). Verify whether Nancy's claim is valid or invalid.

Mathematics
Nancy and her family used 22,5 kl of water in March 2025 and were charged R371,80 (incl VAT). Verify whether Nancy's claim is valid or invalid.

ScanSolve AI Answer

2.1
Tariff is the price per kilolitre (R/k\L) charged for water used in each block.

2.2
Block 2 ranges from >6>6 kL to 10 kL.
Maximum amount of water charged in Block 2:
10kL6kL=4kL10\,kL - 6\,kL = 4\,\mathrm{kL}
4 \mathrm{kL}

2.3
Invalid

2.4

Step 1: Determine water in each block for 15 kL total usage.

Block 1: First 66 kL at R10.5310.53/kL.

Block 2: Next water up to 10 kL total, so 10kL6kL=4kL10\,kL - 6\,kL = 4\,\mathrm{kL} at R12.5812.58/kL.

Block 3: Remaining 15kL10kL=5kL15\,kL - 10\,kL = 5\,\mathrm{kL} at R19.3019.30/kL.

Amount in Block 2 = 44 kL 3.5\neq 3.5 kL (Nancy's claim).

Step 2: Calculate correct charge for Block 2.

Charge=4kL×R12.58/kL=4×12.58=50.32\begin{align*} &Charge &= &\, 4\,kL \times R12.58/kL \\ &= &\, 4 \times 12.58 \\ &= &\, 50.32 \end{align*}

Correct Block 2 charge = R50.3250.32 \neq R40.7040.70 (Nancy's claim).

Step 3: (For completeness) Correct total bill.

Block 1:

Charge=6kL×R10.53/kL=6×10.53=63.18\begin{align*} &Charge &= &\, 6\,kL \times R10.53/kL \\ &= &\, 6 \times 10.53 \\ &= &\, 63.18 \end{align*}

Block 2: R50.3250.32 (from Step 2).

Block 3:

Charge=5kL×R19.30/kL=5×19.30=96.50\begin{align*} &Charge &= &\, 5\,kL \times R19.30/kL \\ &= &\, 5 \times 19.30 \\ &= &\, 96.50 \end{align*}

Total:

Totalcharge=R63.18+R50.32+R96.50=210.00\begin{align*} &Total charge &= &\, R63.18 + R50.32 + R96.50 \\ &= &\, 210.00 \end{align*}

Actual charged = R146.70146.70 \neq R210.00210.00.

Nancy's claim about 3.5 kL at R40.7040.70 (incl VAT) for Block 2 is invalid.
\text{Invalid}

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