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: Calculate the number of boys who have paid their school fees. The total number of boys is 1200, and 50% of them have paid. Boys who paid = 0.50 × 1200 = 600 Step 2: Define variables for the number of girls and the total population. Let G be the number of girls in the school. The total population of students, T, is the sum of boys and girls. T = 1200 + G Step 3: Express the number of students who paid fees in terms of G. 40% of the girls have paid their fees: Girls who paid = 0.40 × G The total number of students who paid fees is 46% of the total population: Total paid = 0.46 × T = 0.46 × (1200 + G) Step 4: Set up an equation based on the total number of students who paid fees. The total number of students who paid fees is also the sum of boys who paid and girls who paid. Total paid = Boys who paid + Girls who paid 0.46 × (1200 + G) = 600 + 0.40G Step 5: Solve the equation for G. Distribute 0.46 on the left side: 0.46 × 1200 + 0.46G = 600 + 0.40G 552 + 0.46G = 600 + 0.40G Subtract 0.40G from both sides: 552 + 0.46G - 0.40G = 600 552 + 0.06G = 600 Subtract 552 from both sides: 0.06G = 600 - 552 0.06G = 48 Divide by 0.06: G = (48)/(0.06) G = 800 The number of girls is 800. The number of girls is 800. That's 2 down. 3 left today — send the next one.