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.
ScanSolve AI Answer
Here are the solutions to the problems: 1.1 Ratio Problems 1.1.1 Divide 45 in the ratio 2:3. Step 1: Find the total number of parts in the ratio. 2 + 3 = 5 Step 2: Determine the value of one part. (45)/(5) = 9 Step 3: Calculate the value for each part of the ratio. 2 × 9 = 18 3 × 9 = 27 The two parts are 18 and 27. 18 and 27 1.1.2 Divide 228 in the ratio 3:5:11. Step 1: Find the total number of parts in the ratio. 3 + 5 + 11 = 19 Step 2: Determine the value of one part. (228)/(19) = 12 Step 3: Calculate the value for each part of the ratio. 3 × 12 = 36 5 × 12 = 60 11 × 12 = 132 The three parts are 36, 60, and 132. 36, 60, and 132 1.1.3 Jan gives R2,50, Paul gives R3,50 and Peter gives R5,00 to buy a packet of sweets. How should they divide the sweets if there are 33 sweets in the packet? Step 1: Determine the ratio of their contributions. 2.50 : 3.50 : 5.00 Multiply by 10 to remove decimals, then simplify by dividing by 5. 25 : 35 : 50 5 : 7 : 10 Step 2: Find the total number of parts in the simplified ratio. 5 + 7 + 10 = 22 Step 3: Calculate the number of sweets per part. 33 sweets22 parts = 1.5 sweets/part Step 4: Distribute the sweets according to the ratio. • Jan: 5 × 1.5 = 7.5 sweets • Paul: 7 × 1.5 = 10.5 sweets • Peter: 10 × 1.5 = 15 sweets They should divide the sweets in the ratio 5:7:10, which means Jan gets 7.5 sweets, Paul gets 10.5 sweets, and Peter gets 15 sweets. Jan: 7.5 sweets, Paul: 10.5 sweets, Peter: 15 sweets 1.2 Increase/Decrease by a Ratio 1.2.1 Decrease 150 in the ratio 4:5. Step 1: Multiply the original value by the ratio, with the "decrease" part (smaller number) in the numerator. New value = 150 × (4)/(5) Step 2: Calculate the new value. New value = 30 × 4 = 120 The new value is 120. 120 1.2.2 Increase 210 in the ratio 9:7. Step 1: Multiply the original value by the ratio, with the "increase" part (larger number) in the numerator. New value = 210 × (9)/(7) Step 2: Calculate the new value. New value = 30 × 9 = 270 The new value is 270. 270 1.2.3 The price of a health bread costing R12,90 is increased in the ratio 15:17. Calculate the new price of the bread. Step 1: Identify the original and new ratio parts. Since the price is increased, the original price corresponds to 15 parts and the new price to 17 parts. New price = Original price × (17)/(15) Step 2: Substitute the original price and calculate the new price. New price = R12.90 × (17)/(15) New price = R0.86 × 17 = R14.62 The new price of the bread is R14,62. R14,62 1.2.4 Petrol costs R11,40 per litre. The price is reduced in the ratio 18:19. Calculate the new price. Step 1: Identify the original and new ratio parts. Since the price is reduced, the original price corresponds to 19 parts and the new price to 18 parts. New price = Original price × (18)/(19) Step 2: Substitute the original price and calculate the new price. New price = R11.40 × (18)/(19) New price = R0.60 × 18 = R10.80 The new price of petrol is R10,80. R10,80 1.3 Speed, Distance, and Time Calculations 1.3.1 A car travelling at a constant speed covers 75 km in 40 minutes. How long will it take to cover a distance of 225 km at the same average speed? Step 1: Calculate the speed of the car. Speed = DistanceTime = 75 km40 min Step 2: Use the speed to find the time required for the new distance. Time