Mariam's Pay: a) Determine the number of extra hours she taught. b) Calculate her total pay for the month. c) Find the total deduction made before tax.

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Asked on April 13, 2026Business/Management

This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.

Accepted Answer · 2026-04-13T20:10:06.338Z

You're on a roll — here's the solution for question 1 from Section B. 1 (i) Mariam's Pay a) Determine the number of extra hours she taught. Step 1: Identify total hours and normal hours. Total hours worked = 50 hours. Normal contracted hours = 36 hours. Step 2: Calculate extra hours. Extra hours = Total hours - Normal hours Extra hours = 50 - 36 = 14 hours The number of extra hours she taught is 14 hours. b) Calculate her total pay for the month. Step 1: Calculate pay for normal hours. Normal rate = 4,500 FCFA/hour. Pay for normal hours = 36 hours × 4,500 FCFA/hour = 162,000 FCFA Step 2: Calculate the rate for extra hours. Extra hour rate = 150\% of normal rate = 1.50 × 4,500 FCFA/hour = 6,750 FCFA/hour . Step 3: Calculate pay for extra hours. Pay for extra hours = 14 hours × 6,750 FCFA/hour = 94,500 FCFA Step 4: Calculate total pay. Total pay = Pay for normal hours + Pay for extra hours Total pay = 162,000 FCFA + 94,500 FCFA = 256,500 FCFA Her total pay for the month is 256,500 FCFA. c) Find the total deduction made before tax. Step 1: Calculate pension deduction. Pension deduction = 5\% of total pay = 0.05 × 256,500 FCFA = 12,825 FCFA . Step 2: Identify Social Insurance deduction. Social Insurance deduction = 15,000 FCFA. Step 3: Calculate total deduction. Total deduction = Pension deduction + Social Insurance deduction Total deduction = 12,825 FCFA + 15,000 FCFA = 27,825 FCFA The total deduction made before tax is 27,825 FCFA. d) Find the income that was taxed. Step 1: Calculate income after deductions. Income after deductions = Total pay - Total deduction Income after deductions = 256,500 FCFA - 27,825 FCFA = 228,675 FCFA Step 2: Subtract the tax-free amount. Tax-free amount = 50,000 FCFA. Taxable income = Income after deductions - Tax-free amount Taxable income = 228,675 FCFA - 50,000 FCFA = 178,675 FCFA The income that was taxed is 178,675 FCFA. e) Find the tax paid. Step 1: Calculate tax paid. Tax rate = 10\%. Tax paid = 10\% of Taxable income Tax paid = 0.10 × 178,675 FCFA = 17,867.50 FCFA The tax paid is 17,867.50 FCFA. 1 (ii) Polynomial f(x) = 2x^3 + x^2 - 18x + 9 a) Show that (x+3) is a factor of f(x). Step 1: Apply the Factor Theorem. According to the Factor Theorem, if (x+3) is a factor of f(x), then f(-3) must be equal to 0. Substitute x=-3 into f(x): f(-3) = 2(-3)^3 + (-3)^2 - 18(-3) + 9 f(-3) = 2(-27) + 9 + 54 + 9 f(-3) = -54 + 9 + 54 + 9 f(-3) = 0 Since f(-3)=0, (x+3) is a factor of f(x). b) Factorise f(x) completely. Step 1: Perform polynomial division to divide f(x) by (x+3). Using synthetic division: ` -3 | 2 1 -18 9 | -6 15 -9 ----------------- 2 -5 -3 0 ` The quotient is 2x^2 - 5x - 3. So, f(x) = (x+3)(2x^2 - 5x - 3). Step 2: Factorise the quadratic factor 2x^2 - 5x - 3. We look for two numbers that multiply to 2 × (-3) = -6 and add to -5. These numbers are -6 and 1. Rewrite the middle term: 2x^2 - 6x + x - 3 Factor by grouping: 2x(x-3) + 1(x-3) (2x+1)(x-3) Step 3: Write the complete factorisation of f(x). f(x) = (x+3)(2x+1)(x-3) The complete factorisation of f(x) is (x+3)(2x+1)(x-3). What's next?

Accepted Answer · 2026-04-13T20:10:06.338Z

You're on a roll — here's the solution for question 1 from Section B. 1 (i) Mariam's Pay a) Determine the number of extra hours she taught. Step 1: Identify total hours and normal hours. Total hours worked = 50 hours. Normal contracted hours = 36 hours. Step 2: Calculate extra hours. Extra hours = Total hours - Normal hours Extra hours = 50 - 36 = 14 hours The number of extra hours she taught is 14 hours. b) Calculate her total pay for the month. Step 1: Calculate pay for normal hours. Normal rate = 4,500 FCFA/hour. Pay for normal hours = 36 hours × 4,500 FCFA/hour = 162,000 FCFA Step 2: Calculate the rate for extra hours. Extra hour rate = 150\% of normal rate = 1.50 × 4,500 FCFA/hour = 6,750 FCFA/hour . Step 3: Calculate pay for extra hours. Pay for extra hours = 14 hours × 6,750 FCFA/hour = 94,500 FCFA Step 4: Calculate total pay. Total pay = Pay for normal hours + Pay for extra hours Total pay = 162,000 FCFA + 94,500 FCFA = 256,500 FCFA Her total pay for the month is 256,500 FCFA. c) Find the total deduction made before tax. Step 1: Calculate pension deduction. Pension deduction = 5\% of total pay = 0.05 × 256,500 FCFA = 12,825 FCFA . Step 2: Identify Social Insurance deduction. Social Insurance deduction = 15,000 FCFA. Step 3: Calculate total deduction. Total deduction = Pension deduction + Social Insurance deduction Total deduction = 12,825 FCFA + 15,000 FCFA = 27,825 FCFA The total deduction made before tax is 27,825 FCFA. d) Find the income that was taxed. Step 1: Calculate income after deductions. Income after deductions = Total pay - Total deduction Income after deductions = 256,500 FCFA - 27,825 FCFA = 228,675 FCFA Step 2: Subtract the tax-free amount. Tax-free amount = 50,000 FCFA. Taxable income = Income after deductions - Tax-free amount Taxable income = 228,675 FCFA - 50,000 FCFA = 178,675 FCFA The income that was taxed is 178,675 FCFA. e) Find the tax paid. Step 1: Calculate tax paid. Tax rate = 10\%. Tax paid = 10\% of Taxable income Tax paid = 0.10 × 178,675 FCFA = 17,867.50 FCFA The tax paid is 17,867.50 FCFA. 1 (ii) Polynomial f(x) = 2x^3 + x^2 - 18x + 9 a) Show that (x+3) is a factor of f(x). Step 1: Apply the Factor Theorem. According to the Factor Theorem, if (x+3) is a factor of f(x), then f(-3) must be equal to 0. Substitute x=-3 into f(x): f(-3) = 2(-3)^3 + (-3)^2 - 18(-3) + 9 f(-3) = 2(-27) + 9 + 54 + 9 f(-3) = -54 + 9 + 54 + 9 f(-3) = 0 Since f(-3)=0, (x+3) is a factor of f(x). b) Factorise f(x) completely. Step 1: Perform polynomial division to divide f(x) by (x+3). Using synthetic division: ` -3 | 2 1 -18 9 | -6 15 -9 ----------------- 2 -5 -3 0 ` The quotient is 2x^2 - 5x - 3. So, f(x) = (x+3)(2x^2 - 5x - 3). Step 2: Factorise the quadratic factor 2x^2 - 5x - 3. We look for two numbers that multiply to 2 × (-3) = -6 and add to -5. These numbers are -6 and 1. Rewrite the middle term: 2x^2 - 6x + x - 3 Factor by grouping: 2x(x-3) + 1(x-3) (2x+1)(x-3) Step 3: Write the complete factorisation of f(x). f(x) = (x+3)(2x+1)(x-3) The complete factorisation of f(x) is (x+3)(2x+1)(x-3). What's next?

Mariam's Pay: a) Determine the number of extra hours she taught. b) Calculate her total pay for the month. c) Find the total deduction made before tax.

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Mariam's Pay: a) Determine the number of extra hours she taught. b) Calculate her total pay for the month. c) Find the total deduction made before tax.

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