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.
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Here are the solutions to the problems: 1. Ebimo deposited an amount of N150,000.00 at a bank with an annual simple interest rate of 5\% for 5 years. What is the interest value? Step 1: Identify the given values. Principal (P) = N150,000 Rate (R) = 5\% = (5)/(100) = 0.05 Time (T) = 5 years Step 2: Use the simple interest formula I = P × R × T. I = 150,000 × 0.05 × 5 Step 3: Calculate the interest. I = 150,000 × 0.25 I = 37,500 The interest value is N37,500. Answer: N37,500 2. The area of a rectangular shop is 24(2)/(3) m^2. If the width of the shop is 3(1)/(3) m, what is the length of the shop? Step 1: Convert the mixed numbers to improper fractions. Area (A) = 24(2)/(3) = ((24 × 3) + 2)/(3) = (72 + 2)/(3) = (74)/(3) m^2 Width (W) = 3(1)/(3) = ((3 × 3) + 1)/(3) = (9 + 1)/(3) = (10)/(3) m Step 2: Use the formula for the area of a rectangle, A = L × W, and rearrange to find the length (L). L = (A)/(W) Step 3: Substitute the values and calculate the length. L = (74)/(3)(10)/(3) L = (74)/(3) × (3)/(10) L = (74)/(10) L = (37)/(5) L = 7(2)/(5) m The length of the shop is 7(2)/(5) m. Answer: 7(2)/(5) m 3. If the number 200 is 125\% of 160, then what percent of 200 is 160? Step 1: Verify the given statement. 125\% of 160 = (125)/(100) × 160 = 1.25 × 160 = 200. The statement is true. Step 2: Set up an equation to find what percent of 200 is 160. Let the unknown percentage be x. x\% of 200 = 160 (x)/(100) × 200 = 160 Step 3: Solve for x. 2x = 160 x = (160)/(2) x = 80 So, 80\% of 200 is 160. Answer: 80\% 4. A student thinks of a number. He multiplies this number by 4, subtracts 20 from the result, and the answer is 36. What is the number? Step 1: Let the unknown number be x. Step 2: Translate the problem into an algebraic equation. Multiplying the number by 4 gives 4x. Subtracting 20 from the result gives 4x - 20. The answer is 36, so: 4x - 20 = 36 Step 3: Solve the equation for x. Add 20 to both sides of the equation: 4x = 36 + 20 4x = 56 Step 4: Divide both sides by 4: x = (56)/(4) x = 14 The number is 14. Answer: 14 3 done, 2 left today. You're making progress.