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. Step 1: Calculate the amount of raw material used in the first step. Material in first step = (2)/(5) × 500 kg Material in first step = (1000)/(5) kg = 200 kg Step 2: Calculate the amount of raw material used in the second step. Material in second step = (3)/(5) × 500 kg Material in second step = (1500)/(5) kg = 300 kg The company uses 200 kg in the first step and 300 kg in the second step. The amount of raw material used in each step is First step: 200 kg, Second step: 300 kg. 2. Step 1: Mary has (1)/(4) of a cake. She gives half of this amount to her sister. To find the fraction her sister receives, multiply Mary's fraction by (1)/(2). Fraction for sister = (1)/(4) × (1)/(2) Step 2: Multiply the numerators and the denominators. Fraction for sister = (1 × 1)/(4 × 2) = (1)/(8) Mary's sister receives (1)/(8) of the cake. The fraction of the cake her sister receives is (1)/(8). 3. Step 1: Royce bought 20 t-shirts. The fraction of large size t-shirts is (3)/(5). To find the number of large t-shirts, multiply the total number of t-shirts by this fraction. Number of large t-shirts = (3)/(5) × 20 Step 2: Perform the multiplication. Number of large t-shirts = (3 × 20)/(5) = (60)/(5) = 12 Royce bought 12 large size t-shirts. The number of large size t-shirts Royce bought is 12. 4. Step 1: Calculate the earnings for the first three days to identify the pattern. Day 1: (1)/(3) × P150.00 = P50.00 Day 2: (2)/(3) × P300.00 = P200.00 Day 3: (4)/(3) × P600.00 = P800.00 Step 2: Observe the pattern in the multipliers and the base amounts. The numerator of the fraction doubles each day (1 2 4). The base amount doubles each day (P150 P300 P600). Step 3: Apply the pattern to find the earnings for the 4th day. For Day 4, the numerator will be 4 × 2 = 8, so the fraction is (8)/(3). For Day 4, the base amount will be P600 × 2 = P1200.00. Step 4: Calculate the earnings for the 4th day. Earnings for Day 4 = (8)/(3) × P1200.00 Earnings for Day 4 = 8 × P1200.003 = 8 × P400.00 = P3200.00 Her daughter earned P3200.00 for the 4th day's work. The amount her daughter earned for the 4th day's work is P3200.00. 5. Step 1: Calculate the fraction of red and yellow clips. Fraction red = (1)/(4) Fraction yellow = (1)/(4) Total fraction of red and yellow = (1)/(4) + (1)/(4) = (2)/(4) = (1)/(2) Step 2: Calculate the fraction of blue clips. The remaining clips are blue. Fraction blue = 1 - Fraction of red and yellow Fraction blue = 1 - (1)/(2) = (1)/(2) Step 3: Calculate the number of blue clips from the total of 60 clips. Number of blue clips = (1)/(2) × 60 Number of blue clips = 30 There are 30 blue clips. The number of blue clips is 30. 3 done, 2 left today. You're making progress.