for the tariff on LEVEL 4 if a household used an amount of water that is above 20 kℓ up to 35 kℓ (Step 4).
This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Step 1: Answer Question 1.1.
The question asks for the tariff on LEVEL 4 if a household used an amount of water that is above 20 kℓ up to 35 kℓ (Step 4).
Looking at the table:
Go to the "STEP" column and find "4".
The "VOLUME/AMOUNT OF WATER USED" for Step 4 is "above 20 kℓ up to 35 kℓ".
Go to the "LEVEL 4 R/kℓ" column for Step 4.
The tariff is R43,69.
The tariff on Level 4 for Step 4 is $\boxed{\text{R}43.69/\text{k}\ell}$.
Step 2: Answer Question 1.2.
The question asks in which STEP/INTERVAL you will pay R52,44 on Level 6.
Looking at the table:
Go to the "LEVEL 6 R/kℓ" column.
Find the value R52,44.
This value corresponds to "STEP 2".
You will pay R52,44 on Level 6 in $\boxed{\text{STEP 2}}$.
Step 3: Answer Question 1.3.
The question asks to calculate the VAT exclusive tariff of STEP 1 of Level 6.
From the table, the tariff for STEP 1 of Level 6 is R29,93/kℓ.
The table states that the rates are "INCLUDING VAT - 15%".
To find the VAT exclusive tariff, divide the VAT inclusive tariff by $(1 + \text{VAT rate})$.
$$\text{VAT exclusive tariff} = \frac{\text{R}29.93}{1 + 0.15} = \frac{\text{R}29.93}{1.15} = \text{R}26.02608...$$
Rounding to two decimal places: R26.03.
The VAT exclusive tariff of STEP 1 of Level 6 is $\boxed{\text{R}26.03/\text{k}\ell}$.
Step 4: Answer Question 1.4.
The question asks to calculate the amount a household will have to pay on Level 4 for consuming 15 kℓ.
We need to calculate the cost for each step up to 15 kℓ on Level 4.
Step 1: 0 kℓ to 6 kℓ. Volume used: 6 kℓ. Tariff: R4,65/kℓ.
Cost for Step 1 = $6 \text{ k}\ell \times \text{R}4.65/\text{k}\ell = \text{R}27.90$
Step 2: above 6 kℓ to 10 kℓ. Volume used: $10 - 6 = 4$ kℓ. Tariff: R17,75/kℓ.
Cost for Step 2 = $4 \text{ k}\ell \times \text{R}17.75/\text{k}\ell = \text{R}71.00$
Step 3: above 10 kℓ up to 20 kℓ. Remaining volume needed: $15 - 10 = 5$ kℓ. Tariff: R25,97/kℓ.
Cost for Step 3 = $5 \text{ k}\ell \times \text{R}25.97/\text{k}\ell = \text{R}129.85$
Total cost for 15 kℓ on Level 4 = Cost Step 1 + Cost Step 2 + Cost Step 3
Total cost = $\text{R}27.90 + \text{R}71.00 + \text{R}129.85 = \text{R}228.75$
The household will have to pay $\boxed{\text{R}228.75}$ on Level 4 for consuming 15 kℓ.
Step 5: Answer Question 1.5.
The question asks to calculate the amount a household will have to pay on Level 6 for consuming 23 kℓ.
We need to calculate the cost for each step up to 23 kℓ on Level 6.
Step 1: 0 kℓ to 6 kℓ. Volume used: 6 kℓ. Tariff: R29,93/kℓ.
Cost for Step 1 = $6 \text{ k}\ell \times \text{R}29.93/\text{k}\ell = \text{R}179.58$
Step 2: above 6 kℓ to 10 kℓ. Volume used: $10 - 6 = 4$ kℓ. Tariff: R52,44/kℓ.
Cost for Step 2 = $4 \text{ k}\ell \times \text{R}52.44/\text{k}\ell = \text{R}209.76$
Step 3: above 10 kℓ up to 20 kℓ. Volume used: $20 - 10 = 10$ kℓ. Tariff: R114,00/kℓ.
Cost for Step 3 = $10 \text{ k}\ell \times \text{R}114.00/\text{k}\ell = \text{R}1140.00$
Step 4: above 20 kℓ up to 35 kℓ. Remaining volume needed: $23 - 20 = 3$ kℓ. Tariff: R134,00/kℓ.
Cost for Step 4 = $3 \text{ k}\ell \times \text{R}134.00/\text{k}\ell = \text{R}402.00$
Total cost for 23 kℓ on Level 6 = Cost Step 1 + Cost Step 2 + Cost Step 3 + Cost Step 4
Total cost = $\text{R}179.58 + \text{R}209.76 + \text{R}1140.00 + \text{R}402.00 = \text{R}1931.34$
The household will have to pay $\boxed{\text{R}1931.34}$ on Level 6 for consuming 23 kℓ.
Step 6: Answer Question 1.6.
The question asks to calculate how much more a household will pay on Level 6 compared to Level 4 for consuming 37 kℓ.
First, calculate the cost for 37 kℓ on Level 4 and Level 6.
Cost for 37 kℓ on Level 4:
Step 1 (0-6 kℓ): $6 \text{ k}\ell \times \text{R}4.65/\text{k}\ell = \text{R}27.90$
Step 2 (6-10 kℓ): $4 \text{ k}\ell \times \text{R}17.75/\text{k}\ell = \text{R}71.00$
Step 3 (10-20 kℓ): $10 \text{ k}\ell \times \text{R}25.97/\text{k}\ell = \text{R}259.70$
Step 4 (20-35 kℓ): $15 \text{ k}\ell \times \text{R}43.69/\text{k}\ell = \text{R}655.35$
Step 5 (35-50 kℓ): Remaining volume: $37 - 35 = 2$ kℓ. Tariff: R113,99/kℓ.
Cost for Step 5 = $2 \text{ k}\ell \times \text{R}113.99/\text{k}\ell = \text{R}227.98$
Total cost Level 4 = $\text{R}27.90 + \text{R}71.00 + \text{R}259.70 + \text{R}655.35 + \text{R}227.98 = \text{R}1241.93$
Cost for 37 kℓ on Level 6:
Step 1 (0-6 kℓ): $6 \text{ k}\ell \times \text{R}29.93/\text{k}\ell = \text{R}179.58$
Step 2 (6-10 kℓ): $4 \text{ k}\ell \times \text{R}52.44/\text{k}\ell = \text{R}209.76$
Step 3 (10-20 kℓ): $10 \text{ k}\ell \times \text{R}114.00/\text{k}\ell = \text{R}1140.00$
Step 4 (20-35 kℓ): $15 \text{ k}\ell \times \text{R}134.00/\text{k}\ell = \text{R}2010.00$
Step 5 (35-50 kℓ): Remaining volume: $37 - 35 = 2$ kℓ. Tariff: R912,00/kℓ.
Cost for Step 5 = $2 \text{ k}\ell \times \text{R}912.00/\text{k}\ell = \text{R}1824.00$
Total cost Level 6 = $\text{R}179.58 + \text{R}209.76 + \text{R}1140.00 + \text{R}2010.00 + \text{R}1824.00 = \text{R}5363.34$
Difference in cost:
Difference = Total cost Level 6 - Total cost Level 4
Difference = $\text{R}5363.34 - \text{R}1241.93 = \text{R}4121.41$
A household will pay $\boxed{\text{R}4121.41}$ more on Level 6 compared to Level 4 for consuming 37 kℓ.
3 done, 2 left today. You're making progress.
