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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Welcome back — been a while! Let's pick up where you left off. Question 1: Step 1: Find the cost of one pair of shoes. Cost of 6 pairs = N1,350 Cost of 1 pair = (1350)/(6) = N225 Step 2: Find the cost of nine pairs of shoes. Cost of 9 pairs = 9 × 225 = N2025 The correct option is A. A. N2,025 Question 2: Step 1: Identify the capacity of one bucket. Capacity of 1 bucket = 5 litres Step 2: Calculate the capacity of 7 buckets. Capacity of 7 buckets = 7 × 5 = 35 litres The correct option is B. B. 35 litres Question 3: Step 1: Identify the ratio and the smallest share. The ratio is 5:3:2. The smallest ratio part is 2. The share corresponding to the smallest ratio (2) is 25 apples. Step 2: Find the value of one ratio part. If 2 parts = 25 apples, then 1 part = (25)/(2) = 12.5 apples. Step 3: Find the total number of apples shared. Total ratio parts = 5 + 3 + 2 = 10 parts. Total apples shared = 10 × 12.5 = 125 apples. The correct option is C. C. 125 Question 4: Step 1: Identify the amounts of sugar used. Sugar for baking = 587 kg (assuming 'kb' is a typo for 'kg') Sugar for coating = 140 kg Step 2: Calculate the total sugar content. Total sugar = 587 kg + 140 kg = 727 kg The correct option is B. B. 727kg Question 5: Step 1: Write the given ratio. Ratio = 15:25 Step 2: Find the greatest common divisor (GCD) of 15 and 25. The GCD of 15 and 25 is 5. Step 3: Divide both parts of the ratio by the GCD. (15)/(5) : (25)/(5) = 3:5 The correct option is B. B. 3:5 Question 6: Step 1: Convert mixed numbers to improper fractions. 5(1)/(4) = ((5 × 4) + 1)/(4) = (21)/(4) 2(1)/(2) = ((2 × 2) + 1)/(2) = (5)/(2) Step 2: Rewrite the expression with improper fractions. (21)/(4) - (5)/(2) + (1)/(4) Step 3: Find a common denominator, which is 4. (21)/(4) - (5 × 2)/(2 × 2) + (1)/(4) = (21)/(4) - (10)/(4) + (1)/(4) Step 4: Perform the addition and subtraction. (21 - 10 + 1)/(4) = (11 + 1)/(4) = (12)/(4) = 3 Step 5: Convert the result back to a mixed number if necessary. 3 = 3(0)/(4) or 3(1)/(2) is not correct. Let's recheck the options. Option B is 3(1)/(2). This is incorrect. Let's recheck the calculation. 5(1)/(4) - 2(1)/(2) + (1)/(4) = (5 + (1)/(4)) - (2 + (1)/(2)) + (1)/(4) = 5 - 2 + (1)/(4) - (1)/(2) + (1)/(4) = 3 + (1)/(4) - (2)/(4) + (1)/(4) = 3 + (1 - 2 + 1)/(4) = 3 + (0)/(4) = 3 None of the options A, B, C, D match 3. Let's assume there might be a typo in the question or options, or I might have misread the options. A. 2(1)/(2) B. 3(1)/(2) C. 1(1)/(2) D. 4(1)/(2) If the answer is exactly 3, then none of the options are correct. However, if we consider the closest option or if there's a slight miscalculation in the options provided. Let's re-evaluate the calculation carefully. 5(1)/(4) - 2(1)/(2) + (1)/(4) = (21)/(4) - (10)/(4) + (1)/(4) = (21 - 10 + 1)/(4) = (11 + 1)/(4) = (12)/(4) = 3 The calculation is consistently 3. Since 3 is not an option, there might be an error in the question or options. If I had to choose the closest, it would be 2(1)/(2) or 3(1)/(2). However, I must provide an answer from the given options. Let me check if there's any common mistake that leads to one of the options. If it was 5(1)/(4) - 2(1)/(4) + (1)/(2) = 3 + (1)/(2) = 3(1)/(2). But it's 2(1)/(2). If it was 5(1)/(4) - 2(1)/(2) - (1)/(4) = (21-10-1)/(4) = (10)/(4) = 2(1)/(2). But it's +(1)/(4). Given the options, and the exact calculation of 3, I cannot confidently select an option. However, if forced to choose, and assuming a slight error in the question or options, I will state the calculated answer. Since I must select from the given options, and my calculation is exactly 3, which is not an option, I will state that the calculated answer is 3 and none of the options match. However, the instruction is to select from the given options. This is a dilemma. I will state the calculated answer and then indicate the closest option if there is one. The calculated answer is 3. Let's check the options: A. 2(1)/(2) = 2.5 B. 3(1)/(2) = 3.5 C. 1(1)/(2) = 1.5 D. 4(1)/(2) = 4.5 The closest option to 3 is 2(1)/(2) or 3(1)/(2). Without further clarification, I cannot definitively choose. I will assume there might be a typo in the question and proceed with the exact calculation. My calculation is 3. Since I must choose an option, and 3 is not present, I will state that the exact answer is 3. Let me re-read the instructions: "When the question includes labeled options (A/B/C/D or 1/2/3/4), you MUST select from the given options. State the correct letter/number first, then explain why. Never give an answer that isn't one of the listed options." This means I must pick one. This implies there might be a common error that leads to one of the options, or a misinterpretation of the question. Let's re-examine the problem: 5(1)/(4) - 2(1)/(2) + (1)/(4). 5.25 - 2.5 + 0.25 = 2.75 + 0.25 = 3. The calculation is definitely 3. If I have to pick an option, and 3 is not there, it's a flawed question. I will state the calculated answer and then explain the discrepancy. However, the instructions say "Never give an answer that isn't one of the listed options." This is a critical constraint. I cannot say "none of the above" or "the answer is 3". I must pick A, B, C, or D. This implies that one of the options is the intended answer, and my calculation might be wrong, or the question is designed to trick. Let's assume there's a mistake in my calculation or interpretation. 5(1)/(4) - 2(1)/(2) + (1)/(4) = (5 + (1)/(4)) - (2 + (1)/(2)) + (1)/(4) = 5 - 2 + (1)/(4) - (1)/(2) + (1)/(4) = 3 + (1)/(4) - (2)/(4) + (1)/(4) = 3 + (1-2+1)/(4) = 3 + (0)/(4) = 3 The calculation is robustly 3. If I must choose an option, and 3 is not an option, I cannot fulfill the instruction without making an assumption about a typo in the question or options. Let's consider if the question meant 5(1)/(4) - 2(1)/(4) + (1)/(2) Then 3 + (1)/(2) = 3(1)/(2). This is option B. This is a common type of error in exam papers where a sign or number is slightly off. Given the constraint to choose an option, I will assume the question intended to lead to 3(1)/(2) and there was a typo in the second fraction. If the question was 5(1)/(4) - 2(1)/(4) + (1)/(2): 5(1)/(4) - 2(1)/(4) + (1)/(2) = (5-2) + ((1)/(4) - (1)/(4)) + (1)/(2) = 3 + 0 + (1)/(2) = 3(1)/(2). This matches option B. I will proceed with this assumption, stating it clearly. Step 1: Convert mixed numbers to improper fractions. 5(1)/(4) = (21)/(4) 2(1)/(2) = (5)/(2) Step 2: Rewrite the expression with a common denominator of 4. (21)/(4) - (5 × 2)/(2 × 2) + (1)/(4) = (21)/(4) - (10)/(4) + (1)/(4) Step 3: Perform the operations. (21 - 10 + 1)/(4) = (11 + 1)/(4) = (12)/(4) = 3 As calculated, the answer is 3. Since 3 is not among the options, and I must select an option, there is likely a typo in the question. If we assume the second term was 2(1)/(4) instead of 2(1)/(2), then: 5(1)/(4) - 2(1)/(4) + (1)/(2) = (5-2) + ((1)/(4) - (1)/(4)) + (1)/(2) = 3 + 0 + (1)/(2) = 3(1)/(2). This matches option B. I will proceed with this assumption to provide an answer from the options. Assuming the question intended to be 5(1)/(4) - 2(1)/(4) + (1)/(2): Step 1: Group whole numbers and fractions. (5 - 2) + ((1)/(4) - (1)/(4)) + (1)/(2) Step 2: Perform the operations. 3 + 0 + (1)/(2) = 3(1)/(2) The correct option, under this assumption, is B. B. 3(1)/(2) Question 7: Step 1: Set up the percentage calculation. Let x be the percentage. x\% of 0.75 = 0.45 (x)/(100) × 0.75 = 0.45 Step 2: Solve for x. x = (0.45)/(0.75) × 100 x = (45)/(75) × 100 x = (3 × 15)/(5 × 15) × 100 $x = (3)/(5) × 100