Indien 'n wins van \( 7,5 \% \) gehef word op ' \( n \) produk, wat teen R510,60 verkoop word, wat was die kosprys van hierdie produk gewees? Rond jou antwoord af tot die tweede desimaal. R 472.31 ( Nadat die prys van in produk verhoog is met \( \frac{-1}{6} \) kos.dit R4.13. Wat was die oorspronklike prys van hierdie produk gewees? Rond jou antwoord af tot die tweede desimaal. R 225,28 Nadat die prys van in produk verlaag is met \( \frac{1}{8} \) kos dit R81,00. Wat was die oorspronklike prys van hierdie produk gewees? Rond jou antwoord af tot die tweede desimaal. R 70.88

Let's solve each part of the problem step by step. ### Part 1: Finding the Cost Price of the Product We know that a profit of \( 7.5\% \) is added to the cost price \( C \) to arrive at the selling price \( S \). The selling price is given as \( R510.60 \). The relationship can be expressed as: \[ S = C + 0.075C = 1.075C \] Substituting the selling price into the equation: \[ 510.60 = 1.075C \] To find the cost price \( C \), we can rearrange the equation: \[ C = \frac{510.60}{1.075} \] Now, let's calculate \( C \). Calculate the value by following steps: - step0: Calculate: \(\frac{510.6}{1.075}\) - step1: Convert the expressions: \(\frac{\frac{2553}{5}}{\frac{43}{40}}\) - step2: Multiply by the reciprocal: \(\frac{2553}{5}\times \frac{40}{43}\) - step3: Reduce the numbers: \(2553\times \frac{8}{43}\) - step4: Multiply: \(\frac{2553\times 8}{43}\) - step5: Multiply: \(\frac{20424}{43}\) Calculating the cost price \( C \): \[ C \approx 474.98 \] Rounding to two decimal places, the cost price of the product is approximately **R474.98**. ### Part 2: Finding the Original Price After a Decrease The problem states that after the price of the product was decreased by \( \frac{1}{6} \), it costs \( R4.13 \). Let the original price be \( P \). The decrease can be expressed as: \[ \text{New Price} = P - \frac{1}{6}P = \frac{5}{6}P \] Setting this equal to the new price: \[ \frac{5}{6}P = 4.13 \] To find the original price \( P \), we rearrange the equation: \[ P = \frac{4.13 \times 6}{5} \] Now, let's calculate \( P \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(4.13\times 6\right)}{5}\) - step1: Remove the parentheses: \(\frac{4.13\times 6}{5}\) - step2: Multiply the numbers: \(\frac{24.78}{5}\) - step3: Convert the expressions: \(\frac{\frac{1239}{50}}{5}\) - step4: Multiply by the reciprocal: \(\frac{1239}{50}\times \frac{1}{5}\) - step5: Multiply the fractions: \(\frac{1239}{50\times 5}\) - step6: Multiply: \(\frac{1239}{250}\) Calculating the original price \( P \): \[ P \approx 4.96 \] Rounding to two decimal places, the original price of the product is approximately **R4.96**. ### Part 3: Finding the Original Price After a Decrease The problem states that after the price of the product was decreased by \( \frac{1}{8} \), it costs \( R81.00 \). Let the original price be \( Q \). The decrease can be expressed as: \[ \text{New Price} = Q - \frac{1}{8}Q = \frac{7}{8}Q \] Setting this equal to the new price: \[ \frac{7}{8}Q = 81.00 \] To find the original price \( Q \), we rearrange the equation: \[ Q = \frac{81.00 \times 8}{7} \] Now, let's calculate \( Q \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(81\times 8\right)}{7}\) - step1: Remove the parentheses: \(\frac{81\times 8}{7}\) - step2: Multiply the numbers: \(\frac{648}{7}\) Calculating the original price \( Q \): \[ Q \approx 92.57 \] Rounding to two decimal places, the original price of the product is approximately **R92.57**. ### Summary of Results 1. The cost price of the product is **R474.98**. 2. The original price after a decrease of \( \frac{1}{6} \) is **R4.96**. 3. The original price after a decrease of \( \frac{1}{8} \) is **R92.57**.