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's the solution to the problem: Step 1: Define variables for the ages. Let F be Faith's age. Let N be Nabil's age. Step 2: Formulate equations based on the given information. "Nabil is four years older than his sister Faith": N = F + 4 "The product of their ages is 21": N × F = 21 Step 3: Substitute the first equation into the second to form a quadratic equation. Substitute N = F + 4 into N × F = 21: (F + 4)F = 21 F^2 + 4F = 21 F^2 + 4F - 21 = 0 Step 4: Solve the quadratic equation for Faith's age. Factor the quadratic equation: (F + 7)(F - 3) = 0 This gives two possible solutions for F: F = -7 or F = 3 Since age cannot be negative, Faith's age is F = 3 years. Step 5: Determine Nabil's age. Using the equation N = F + 4: N = 3 + 4 N = 7 Nabil's age is 7 years. Step 6: State their ages. Faith's age is 3 years and Nabil's age is 7 years. Faith: 3 years, Nabil: 7 years That's 2 down. 3 left today — send the next one.