Pregunta
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2.1 The price of a toasted cheese sandwich increased from \( R 3,35 \) to \( R 4,00 \). Calculate the increase as a percentage How much will you pay for a T-shirt if it is priced at \( R 120 \) and you are offered a \( 20 \% \% \) discount? 1.3.1 Convert 3000000 mg to \( g \) and then to kg 1.3.2 Convert 36345 seconds to hours, min and seconds Jacob arrives at work at \( 07: 15 \) am and left work at \( 16: 15 \). How long has he workea If he Also took a 30 min break?

Ask by Barnett Lynch. in South Africa
Mar 11,2025

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**1. Sandwich Price Increase:** - The price increased by R0.65, which is approximately 19.4% of the original price. **2. T-Shirt Discount:** - After a 20% discount, the T-shirt costs R96. **3. Unit Conversions:** - 3,000,000 mg is equal to 3,000 grams or 3 kilograms. - 36,345 seconds is equal to 10 hours, 5 minutes, and 45 seconds. **4. Jacob’s Working Time:** - Jacob worked for a total of 8.5 hours, considering a 30-minute break.

Solución

**1. Increase in the price of the toasted cheese sandwich** - **Step 1:** Calculate the increase in price \[ \text{Increase} = R\,4.00 - R\,3.35 = R\,0.65 \] - **Step 2:** Calculate the increase as a percentage of the original price \[ \text{Percentage Increase} = \left(\frac{R\,0.65}{R\,3.35}\right) \times 100 \approx 19.4\% \] --- **2. Price of the T-shirt after a 20\% discount** - **Step 1:** Calculate the discount amount \[ \text{Discount Amount} = 20\% \text{ of } R\,120 = 0.20 \times R\,120 = R\,24 \] - **Step 2:** Calculate the price after discount \[ \text{Discounted Price} = R\,120 - R\,24 = R\,96 \] --- **3. Unit conversions** **3.1 Convert 3000000 mg to \(g\) and then to \(kg\)** - **Step 1:** Convert mg to g \[ 1\,g = 1000\,mg \quad \Rightarrow \quad 3000000\,mg = \frac{3000000}{1000} = 3000\,g \] - **Step 2:** Convert g to kg \[ 1\,kg = 1000\,g \quad \Rightarrow \quad 3000\,g = \frac{3000}{1000} = 3\,kg \] **3.2 Convert 36345 seconds to hours, minutes, and seconds** - **Step 1:** Find the number of hours \[ \text{Hours} = \left\lfloor \frac{36345}{3600} \right\rfloor = 10\, \text{hours} \quad (\text{since } 10 \times 3600 = 36000) \] - **Step 2:** Calculate the remaining seconds \[ \text{Remaining Seconds} = 36345 - 36000 = 345\, \text{seconds} \] - **Step 3:** Convert the remaining seconds into minutes \[ \text{Minutes} = \left\lfloor \frac{345}{60} \right\rfloor = 5\, \text{minutes} \quad (\text{since } 5 \times 60 = 300) \] - **Step 4:** Find the remaining seconds \[ \text{Seconds} = 345 - 300 = 45\, \text{seconds} \] - **Final Answer:** \[ 10\, \text{hours},\ 5\, \text{minutes},\ 45\, \text{seconds} \] --- **4. Jacob’s working time** - **Step 1:** Calculate the total time from arrival to leaving \[ \text{Total Time} = 16:15 - 07:15 = 9\, \text{hours} \] - **Step 2:** Subtract the break time of 30 minutes \[ \text{Actual Working Time} = 9\, \text{hours} - 0.5\, \text{hours} = 8.5\, \text{hours} \quad (\text{or } 8\, \text{hours and } 30\, \text{minutes}) \]

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Bonus Knowledge

To calculate the increase in the price of the toasted cheese sandwich, you first subtract the old price from the new price: \( R 4,00 - R 3,35 = R 0,65 \). To find the percentage increase, divide the increase by the original price and multiply by 100: \( (R 0,65 / R 3,35) \times 100 \approx 19,4\% \). If you have a T-shirt priced at \( R 120 \) and receive a \( 20\% \) discount, you first calculate the amount of the discount: \( R 120 \times 0,20 = R 24 \). Then, subtract the discount from the original price: \( R 120 - R 24 = R 96 \). So, you will pay \( R 96 \) for the T-shirt! To convert \( 3,000,000 \) mg to grams, divide by \( 1000 \) (since there are \( 1000 \) mg in a gram): \( 3,000,000 \, \text{mg} \div 1000 = 3000 \, \text{g} \). Now, to convert grams to kilograms, divide by \( 1000 \) again: \( 3000 \, \text{g} \div 1000 = 3 \, \text{kg} \). When converting seconds into hours, minutes, and seconds, you'll start with \( 36,345 \, \text{seconds} \). There are \( 3600 \) seconds in an hour, so divide \( 36,345 \) by \( 3600 \) to find the hours: \( 36,345 \div 3600 \approx 10 \) hours with a remainder of \( 2345 \) seconds left. Next, convert the leftover seconds into minutes: \( 2345 \div 60 \approx 39 \) minutes, with \( 5 \) seconds remaining. So, \( 36,345 \) seconds equals \( 10 \) hours, \( 39 \) minutes, and \( 5 \) seconds. For Jacob’s working hours, he arrives at \( 07:15 \) am and leaves at \( 16:15 \), giving him a total of \( 9 \) hours worked. Since he took a \( 30 \, \text{min} \) break, you subtract that time: \( 9 \, \text{hours 0} \, \text{minutes} - 0 \, \text{hours 30} \, \text{minutes} = 8 \, \text{hours 30} \, \text{minutes} \).

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