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 the simple interest equations. Let P_1 be the amount invested at 11\% and P_2 be the amount invested at 10\%. The interest rate for the first account is R_1 = 11\% = 0.11. The interest rate for the second account is R_2 = 10\% = 0.10. The time period for both investments is T = 3(1)/(2) years = 3.5 years. The total interest earned is I_total = GH¢ 22,580.60. The formula for simple interest is I = P × R × T. Step 2: Express the relationship between P_1 and P_2. The problem states that the amount invested at 11\% (P_1) is 140\% of the amount invested at 10\% (P_2). P_1 = 140\% × P_2 = 1.4 × P_2 Step 3: Write the total interest equation. The total interest is the sum of the interest from each account: I_total = (P_1 × R_1 × T) + (P_2 × R_2 × T) Substitute the known values: 22,580.60 = (P_1 × 0.11 × 3.5) + (P_2 × 0.10 × 3.5) Step 4: Substitute P_1 in terms of P_2 into the total interest equation and solve for P_2. 22,580.60 = (1.4 P_2 × 0.11 × 3.5) + (P_2 × 0.10 × 3.5) Calculate the products: 1.4 × 0.11 × 3.5 = 0.154 × 3.5 = 0.539 0.10 × 3.5 = 0.35 So the equation becomes: 22,580.60 = 0.539 P_2 + 0.35 P_2 22,580.60 = (0.539 + 0.35) P_2 22,580.60 = 0.889 P_2 Now, solve for P_2: P_2 = (22,580.60)/(0.889) = 25,400 So, P_2 = GH¢ 25,400. Step 5: Calculate the amount invested at 11\% (P_1). Using the relationship P_1 = 1.4 P_2: P_1 = 1.4 × 25,400 P_1 = 35,560 The amount invested at 11\% is GH¢ 35,560. That's 2 down. 3 left today — send the next one.