William earns straight commission as a real-estate agent. Last month his total sales were R971 168, 00. If William earns a 3% rate of commission, what was his total income last month?

Question

Asked on June 15, 2026Mathematics

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.

Accepted Answer · 2026-06-15T19:18:23.573Z

Here are the solutions to the questions: QUESTION 2 2.1 Step 1: Calculate William's commission. Commission = 3% of R971 168.00 Commission = (3)/(100) × 971168 Commission = 0.03 × 971168 Commission = R29 135.04 William's total income last month was his commission. William's total income = R29 135.04 2.2 Step 1: Determine the number of years the money will be invested. Number of years (n) = Daughter's future age - Daughter's current age n = 21 - 17 = 4 years Step 2: Use the compound interest formula A = P(1 + i)^n. Given: Principal (P) = R5 900 Interest rate (i) = 7.5% = 0.075 Number of years (n) = 4 Step 3: Substitute the values into the formula. A = 5900(1 + 0.075)^4 A = 5900(1.075)^4 Step 4: Calculate the future value. A = 5900 × 1.335469140625 A = 7879.2678296875 The amount in the bank when she is 21 years old will be R7 879.27. 2.3 2.3.1 Step 1: Evaluate the powers and division. (-3)^4 - 4 × ((25)/(5))^2 81 - 4 × (5)^2 Step 2: Evaluate the remaining power. 81 - 4 × 25 Step 3: Perform the multiplication. 81 - 100 Step 4: Perform the subtraction. -19 The value is -19. 2.3.2 Step 1: Simplify the terms inside the parenthesis. (sqrt(9) + sqrt((125)/(5))2^4 - sqrt(81))^2 (3 + sqrt(25)16 - 9)^2 Step 2: Continue simplifying the terms. ((3 + 5)/(7))^2 ((8)/(7))^2 Step 3: Square the fraction. (8^2)/(7^2) (64)/(49) The value is (64)/(49). QUESTION 3 3.1 3.1.1 Step 1: Apply the power rule (a^m)^n = a^mn and (ab)^n = a^n b^n. -3(y^-1x^2)^-3 × (yx)^-5 -3(y^(-1) × (-3) x^2 × (-3)) × (y^-5x^-5) -3(y^3 x^-6) × (y^-5x^-5) Step 2: Multiply the terms, combining like bases using a^m a^n = a^m+n. -3 y^3+(-5) x^-6+(-5) -3 y^-2 x^-11 Step 3: Express with positive exponents. -(3)/(y^2 x^11) 3.1.2 Step 1: Simplify the term (1)/(a^-2) to a^2. ((a^2 + a^2)/(a^2 × a^2))^-2 Step 2: Simplify the numerator and denominator inside the parenthesis. ((2a^2)/(a^2+2))^-2 ((2a^2)/(a^4))^-2 Step 3: Simplify the fraction inside the parenthesis using (a^m)/(a^n) = a^m-n. (2a^2-4)^-2 (2a^-2)^-2 Step 4: Apply the outer power of -2. 2^-2 (a^-2)^-2 2^-2 a^(-2) × (-2) 2^-2 a^4 Step 5: Express with positive exponents. (a^4)/(2^2) (a^4)/(4) 3.1.3 Step 1: Expand the product of the two binomials (x-4)(2x+3y) using the FOIL method. 3(x · 2x + x · 3y - 4 · 2x - 4 · 3y) 3(2x^2 + 3xy - 8x - 12y) Step 2: Distribute the 3 to each term inside the parenthesis. 3 × 2x^2 + 3 × 3xy - 3 × 8x - 3 × 12y 6x^2 + 9xy - 24x - 36y 3.1.4 Step 1: Factor out the common term in the numerator of the first fraction. (2x(x - 1))/(x) × (1)/(x^2 - 2x + 1) Step 2: Simplify the first fraction by cancelling x. 2(x - 1) × (1)/(x^2 - 2x + 1) Step 3: Factor the denominator of the second fraction, which is a perfect square trinomial (x-1)^2. 2(x - 1) × (1)/((x - 1)^2) Step 4: Multiply the terms and simplify by cancelling (x-1). (2(x - 1))/((x - 1)^2) (2)/(x - 1) The simplified expression is (2)/(x - 1). 3.2 3.2.1 Step 1: Recognize the expression as a difference of squares, a^2 - b^2 = (a-b)(a+b). Here, a^2 = 16y^2 a = sqrt(16y^2) = 4y. And b^2 = p^2 b = sqrt(p^2) = p. Step 2: Apply the difference of squares formula. (4y - p)(4y + p) 3.2.2 Step 1: Factor the quadratic trinomial x^2 + 9x + 14. We need to find two numbers that multiply to 14 and add up to 9. These numbers are 2 and 7 (2 × 7 = 14 and 2 + 7 = 9). Step 2: Write the factored form. (x + 2)(x + 7) That's 2 down. 3 left today — send the next one.

Accepted Answer · 2026-06-15T19:18:23.573Z

Here are the solutions to the questions: QUESTION 2 2.1 Step 1: Calculate William's commission. Commission = 3% of R971 168.00 Commission = (3)/(100) × 971168 Commission = 0.03 × 971168 Commission = R29 135.04 William's total income last month was his commission. William's total income = R29 135.04 2.2 Step 1: Determine the number of years the money will be invested. Number of years (n) = Daughter's future age - Daughter's current age n = 21 - 17 = 4 years Step 2: Use the compound interest formula A = P(1 + i)^n. Given: Principal (P) = R5 900 Interest rate (i) = 7.5% = 0.075 Number of years (n) = 4 Step 3: Substitute the values into the formula. A = 5900(1 + 0.075)^4 A = 5900(1.075)^4 Step 4: Calculate the future value. A = 5900 × 1.335469140625 A = 7879.2678296875 The amount in the bank when she is 21 years old will be R7 879.27. 2.3 2.3.1 Step 1: Evaluate the powers and division. (-3)^4 - 4 × ((25)/(5))^2 81 - 4 × (5)^2 Step 2: Evaluate the remaining power. 81 - 4 × 25 Step 3: Perform the multiplication. 81 - 100 Step 4: Perform the subtraction. -19 The value is -19. 2.3.2 Step 1: Simplify the terms inside the parenthesis. (sqrt(9) + sqrt((125)/(5))2^4 - sqrt(81))^2 (3 + sqrt(25)16 - 9)^2 Step 2: Continue simplifying the terms. ((3 + 5)/(7))^2 ((8)/(7))^2 Step 3: Square the fraction. (8^2)/(7^2) (64)/(49) The value is (64)/(49). QUESTION 3 3.1 3.1.1 Step 1: Apply the power rule (a^m)^n = a^mn and (ab)^n = a^n b^n. -3(y^-1x^2)^-3 × (yx)^-5 -3(y^(-1) × (-3) x^2 × (-3)) × (y^-5x^-5) -3(y^3 x^-6) × (y^-5x^-5) Step 2: Multiply the terms, combining like bases using a^m a^n = a^m+n. -3 y^3+(-5) x^-6+(-5) -3 y^-2 x^-11 Step 3: Express with positive exponents. -(3)/(y^2 x^11) 3.1.2 Step 1: Simplify the term (1)/(a^-2) to a^2. ((a^2 + a^2)/(a^2 × a^2))^-2 Step 2: Simplify the numerator and denominator inside the parenthesis. ((2a^2)/(a^2+2))^-2 ((2a^2)/(a^4))^-2 Step 3: Simplify the fraction inside the parenthesis using (a^m)/(a^n) = a^m-n. (2a^2-4)^-2 (2a^-2)^-2 Step 4: Apply the outer power of -2. 2^-2 (a^-2)^-2 2^-2 a^(-2) × (-2) 2^-2 a^4 Step 5: Express with positive exponents. (a^4)/(2^2) (a^4)/(4) 3.1.3 Step 1: Expand the product of the two binomials (x-4)(2x+3y) using the FOIL method. 3(x · 2x + x · 3y - 4 · 2x - 4 · 3y) 3(2x^2 + 3xy - 8x - 12y) Step 2: Distribute the 3 to each term inside the parenthesis. 3 × 2x^2 + 3 × 3xy - 3 × 8x - 3 × 12y 6x^2 + 9xy - 24x - 36y 3.1.4 Step 1: Factor out the common term in the numerator of the first fraction. (2x(x - 1))/(x) × (1)/(x^2 - 2x + 1) Step 2: Simplify the first fraction by cancelling x. 2(x - 1) × (1)/(x^2 - 2x + 1) Step 3: Factor the denominator of the second fraction, which is a perfect square trinomial (x-1)^2. 2(x - 1) × (1)/((x - 1)^2) Step 4: Multiply the terms and simplify by cancelling (x-1). (2(x - 1))/((x - 1)^2) (2)/(x - 1) The simplified expression is (2)/(x - 1). 3.2 3.2.1 Step 1: Recognize the expression as a difference of squares, a^2 - b^2 = (a-b)(a+b). Here, a^2 = 16y^2 a = sqrt(16y^2) = 4y. And b^2 = p^2 b = sqrt(p^2) = p. Step 2: Apply the difference of squares formula. (4y - p)(4y + p) 3.2.2 Step 1: Factor the quadratic trinomial x^2 + 9x + 14. We need to find two numbers that multiply to 14 and add up to 9. These numbers are 2 and 7 (2 × 7 = 14 and 2 + 7 = 9). Step 2: Write the factored form. (x + 2)(x + 7) That's 2 down. 3 left today — send the next one.

William earns straight commission as a real-estate agent. Last month his total sales were R971 168, 00. If William earns a 3% rate of commission, what was his total income last month?

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William earns straight commission as a real-estate agent. Last month his total sales were R971 168, 00. If William earns a 3% rate of commission, what was his total income last month?

Need help with your own homework?

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