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 your questions: 1. Mass of the clothes Step 1: Identify the given masses. The mass of the empty bag is m kilograms. The total mass of the bag when full of clothes is 16 kilograms. Step 2: Formulate the relationship between the masses. The total mass is the sum of the mass of the empty bag and the mass of the clothes. Total mass = Mass of empty bag + Mass of clothes 16 = m + Mass of clothes Step 3: Write an expression for the mass of the clothes. To find the mass of the clothes, subtract the mass of the empty bag from the total mass. Mass of clothes = 16 - m The expression to represent the mass of the clothes is: (16 - m) kilograms 2. Solve the equation 6(r+3) = (2r+12) Step 1: Distribute the 6 on the left side of the equation. 6(r+3) = 2r+12 6r + 6 × 3 = 2r+12 6r + 18 = 2r+12 Step 2: Collect terms with r on one side and constant terms on the other side. Subtract 2r from both sides: 6r - 2r + 18 = 12 4r + 18 = 12 Subtract 18 from both sides: 4r = 12 - 18 4r = -6 Step 3: Solve for r. Divide both sides by 4: r = (-6)/(4) r = -(3)/(2) The value of r is: -(3)/(2) That's 2 down. 3 left today — send the next one.