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
Morning precious — let's get this done. Here are the solutions to your homework questions: 1. Step 1: Divide the total number of oranges by the number of pupils. Oranges per pupil = 540 oranges10 pupils Step 2: Calculate the result. Oranges per pupil = 54 Each pupil will have 54 oranges. 54 oranges 2. Step 1: Divide 3500 by 14 to find how many times 14 is contained in 3500. (3500)/(14) Step 2: Perform the division. (3500)/(14) = 250 14 is contained 250 times in 3500. 250 3. Changing them to improper fractions: a) 1 (1)/(4) Step 1: Multiply the whole number by the denominator and add the numerator. Keep the same denominator. 1 (1)/(4) = ((1 × 4) + 1)/(4) Step 2: Simplify the numerator. (4 + 1)/(4) = (5)/(4) (5)/(4) b) 2 (3)/(6) Step 1: Multiply the whole number by the denominator and add the numerator. Keep the same denominator. 2 (3)/(6) = ((2 × 6) + 3)/(6) Step 2: Simplify the numerator. (12 + 3)/(6) = (15)/(6) Step 3: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3. (15 ÷ 3)/(6 ÷ 3) = (5)/(2) (5)/(2) c) 3 (2)/(3) Step 1: Multiply the whole number by the denominator and add the numerator. Keep the same denominator. 3 (2)/(3) = ((3 × 3) + 2)/(3) Step 2: Simplify the numerator. (9 + 2)/(3) = (11)/(3) (11)/(3) d) 6 (3)/(4) Step 1: Multiply the whole number by the denominator and add the numerator. Keep the same denominator. 6 (3)/(4) = ((6 × 4) + 3)/(4) Step 2: Simplify the numerator. (24 + 3)/(4) = (27)/(4) (27)/(4) e) 10 (1)/(4) Step 1: Multiply the whole number by the denominator and add the numerator. Keep the same denominator. 10 (1)/(4) = ((10 × 4) + 1)/(4) Step 2: Simplify the numerator. (40 + 1)/(4) = (41)/(4) (41)/(4) 4. This is an inverse proportion problem: more time means fewer pupils are needed. Step 1: Set up the inverse proportion relationship: P_1 T_1 = P_2 T_2. 27 pupils × 3 hours = P_2 × 6 hours Step 2: Calculate the total "pupil-hours" of work. 81 pupil-hours = P_2 × 6 hours Step 3: Solve for P_2. P_2 = 81 pupil-hours6 hours P_2 = 13.5 Since you can't have half a pupil, and you need enough pupils to eat the food, you would need 14 pupils. (If the question implies minimum whole pupils, it's 14. If it implies exact rate, it's 13.5. Assuming practical application, round up). 14 pupils 5. This is an inverse proportion problem: fewer days mean more men are needed. Step 1: Set up the inverse proportion relationship: M_1 D_1 = M_2 D_2. 6 men × 10 days = M_2 × 3 days Step 2: Calculate the total "man-days" of work. 60 man-days = M_2 × 3 days Step 3: Solve for M_2. M_2 = 60 man-days3 days M_2 = 20 20 men can build the shed in 3 days. 20 men 6. This is a direct proportion problem: if the distance doubles, the time taken will also double at the same rate. Step 1: Identify the given information. D_1 = 50 km, T_1 = 15 hours D_2 = 100 km, T_2 = ? Step 2: Notice that D_2 is twice D_1. D_2 = 2 × D_1 Step 3: Since the rate is the same, T_2 will also be twice T_1. T_2 = 2 × T_1 T_2 = 2 × 15 hours T_2 = 30 hours It will take 30 hours to travel 100 kilometres. 30 hours Send me the next one 📸