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
Step 1: Solve part (a)(i). To divide 24 in the ratio 7:5, first find the total number of parts: Total parts = 7 + 5 = 12 Next, find the value of one part: Value per part = (\24)/(12) = \2 Now, multiply the value per part by each number in the ratio: First share = 7 × \2 = \14 Second share = 5 × \2 = \10 The two amounts are 14 and 10. Step 2: Solve part (a)(ii). To write 24.60 as a fraction of 2870, form the fraction and simplify it. (24.60)/(2870) Multiply the numerator and denominator by 100 to remove the decimal: (24.60 × 100)/(2870 × 100) = (2460)/(287000) Divide both by 10: (246)/(28700) Divide both by 2: (123)/(14350) Recognize that 123 = 3 × 41. Check if 14350 is divisible by 41: 14350 ÷ 41 = 350 So, the fraction can be simplified by dividing both numerator and denominator by 41: (3 × 41)/(350 × 41) = (3)/(350) Step 3: Solve part (a)(iii). To write 1.92 as a percentage of 1.60, divide 1.92 by 1.60 and multiply by 100\%. (1.92)/(1.60) × 100\% (192)/(160) × 100\% Divide both numerator and denominator by 16: (12)/(10) × 100\% 1.2 × 100\% = 120\% Step 4: Solve part (b)(i). The original price is 12, and it is reduced by 15\%. First, calculate the discount amount: Discount = 15\% of \12 = 0.15 × \12 = \1.80 Next, subtract the discount from the original price to find the sale price: Sale price = Original price - Discount Sale price = \12 - \1.80 = \10.20 Alternatively, if the price is reduced by 15\%, the sale price is 100\% - 15\% = 85\% of the original price. Sale price = 85\% of \12 = 0.85 × \12 = \10.20 a) i) The two amounts are \14 and \10. ii) The fraction in its lowest terms is (3)/(350). iii) 1.92 as a percentage of 1.60 is 120\%. b) i) The sale price of the book is \10.20. That's 2 down. 3 left today — send the next one.