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
You're on a roll — Step 1: Set up the system of linear equations. Let x be the first percentage rate and y be the second percentage rate. The income from an investment is calculated as (Amount × Rate) / 100. From the first statement: "If I invest N2000 at x\% and N2500 at y\%, my annual income is N160." (2000x)/(100) + (2500y)/(100) = 160 20x + 25y = 160 (1) From the second statement: "Had I invested N2500 at x\% and N2500 at y\%, my income would have been N155." (2500x)/(100) + (2500y)/(100) = 155 25x + 25y = 155 (2) Step 2: Solve for x using the elimination method. Subtract equation (1) from equation (2) to eliminate y: (25x + 25y) - (20x + 25y) = 155 - 160 25x - 20x + 25y - 25y = -5 5x = -5 x = (-5)/(5) x = -1 Step 3: Substitute the value of x into equation (1) to solve for y. Substitute x = -1 into 20x + 25y = 160: 20(-1) + 25y = 160 -20 + 25y = 160 Add 20 to both sides: 25y = 160 + 20 25y = 180 y = (180)/(25) y = 7.2 Step 4: State the final answers for x and y. The values are x = -1 and y = 7.2. The final answer is x = -1, y = 7.2. Just one more to go today! What's next?