This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey michelle, good to see you again. Here are the solutions to the questions: Worksheet 5 Step 1: Calculate total call time in seconds for 5.1. First, convert each call duration to seconds: 3 min 15 secs = (3 × 60) secs + 15 secs = 180 secs + 15 secs = 195 secs 4 min 30 secs = (4 × 60) secs + 30 secs = 240 secs + 30 secs = 270 secs 0 min 45 secs = 45 secs 0 min 24 secs = 24 secs 12 min 10 secs = (12 × 60) secs + 10 secs = 720 secs + 10 secs = 730 secs 0 min 40 secs = 40 secs Now, sum all the durations: 195 + 270 + 45 + 24 + 730 + 40 = 1304 seconds The total time David talked in the day is 1304 seconds. Step 2: Calculate the cost using the prepaid option for 5.2. The prepaid option costs 6c per second. Total seconds from 5.1 = 1304 seconds. Cost in cents: 1304 secs × 6 c/sec = 7824 cents Convert cents to Rands (1 Rand = 100 cents): 7824 cents100 c/Rand = R78.24 He would have to pay R78.24. Step 3: Determine included minutes for 5.3. The Contract option includes 200 minutes. He gets 200 minutes as part of the Contract option. Step 4: Calculate minutes used on contract for 5.4. For the contract option, calls are billed "per minute or part thereof", meaning each call duration is rounded up to the next whole minute. 3 min 15 secs → 4 minutes 4 min 30 secs → 5 minutes 0 min 45 secs → 1 minute 0 min 24 secs → 1 minute 12 min 10 secs → 13 minutes 0 min 40 secs → 1 minute Sum the rounded-up minutes: 4 + 5 + 1 + 1 + 13 + 1 = 25 minutes He would use up 25 minutes on his contract. Step 5: Answer 5.5 a), b), and c). a) Why does he say that he only has 22 working days in a month (14 + 8 days = 22 days)? He states that he uses his free minutes in 8 working days and pays extra for 14 working days. The sum of these two periods (8 + 14) represents the total number of working days he considers in a month, which is 22 working days. b) He calculates that he will have to pay for an extra 350 minutes of calls per month. How much extra will he have to pay for calls? Extra calls are charged at R1.37 per minute. Extra cost: 350 minutes × R1.37/minute = R479.50 He will have to pay an extra R479.50 for calls. c) Using your answer from question 5.5 b), calculate his total that he would pay per month for the Contract option. Monthly fee for Contract option = R381.90. Extra call cost from 5.5 b) = R479.50. Total monthly cost for Contract option: R381.90 + R479.50 = R861.40 He would pay a total of R861.40 per month for the Contract option. Step 6: Calculate prepaid cost for work calls for 5.6. This question asks for the cost of the calls made in 5.1 if the Prepaid option was used. This is the answer from question 5.2. He would pay R78.24 per month for his calls if he used the Prepaid option. Step 7: Advise on the best option for 5.7. Compare the total monthly costs: Prepaid option (from 5.6): R78.24 Contract option (from 5.5 c): R861.40 The Prepaid option is significantly cheaper for the calls David made. I would advise him to choose the Prepaid option. Reason: The total cost for his calls using the Prepaid option (R78.24) is much lower than the total cost for the Contract option (R861.40), even considering the monthly fee and extra minutes. Worksheet 6 Step 8: Answer 6.1 a) and b). a) How far does she ride in mm? Mary-Jane rides 14.84 km. To convert kilometers to millimeters: 1 km = 1000 m 1 m = 1000 mm So, 1 km = 1000 × 1000 mm = 1,000,000 mm. Distance in mm: 14.84 km × 1,000,000 mm/km = 14,840,000 mm She rides 14,840,000 mm. b) Which unit (km or mm) do you think is best for measuring this distance? Kilometers (km) is the best unit for measuring this distance. Millimeters would result in a very large and impractical number, while kilometers provide a more manageable and understandable value for such a long distance. Step 9: Answer 6.2 a). a) How many ml of orange juice can it hold? The vat holds 4600 L of orange juice. To convert liters to milliliters: 1 L = 1000 ml Volume in ml: 4600 L × 1000 ml/L = 4,600,000 ml It can hold 4,600,000 ml of orange juice. Send me the next one 📸