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: Define variables and set up equations for the initial state. Let B be the initial number of boys and G be the initial number of girls. From the problem statement: The total number of students is 45: B + G = 45 (Equation 1) The number of boys is three times the number of girls: B = 3G (Equation 2) Step 2: Solve for B and G using Equations 1 and 2. Substitute Equation 2 into Equation 1: 3G + G = 45 4G = 45 G = (45)/(4) = 11.25 Now find B: B = 3G = 3 × 11.25 = 33.75 Since the number of students must be whole numbers, these non-integer values indicate that the initial conditions as stated are problematic. We will proceed to check consistency with the second set of conditions. Step 3: Set up equations for the new state. 5 more boys join, so the new number of boys is B' = B + 5. 3 more girls join, so the new number of girls is G' = G + 3. The new number of boys will be twice the new number of girls: B' = 2G' Substitute the expressions for B' and G': B + 5 = 2(G + 3) (Equation 3) Step 4: Substitute the values of B and G from Step 2 into Equation 3. Substitute B = 33.75 and G = 11.25 into Equation 3: 33.75 + 5 = 2(11.25 + 3) 38.75 = 2(14.25) 38.75 = 28.5 Step 5: Conclude based on the contradiction. The statement 38.75 = 28.5 is false. This means that the conditions given in the problem cannot be simultaneously satisfied. Therefore, there is no solution for the initial number of boys and girls that fits all the criteria. No solution Got more? Send 'em!