17. Hassan sells fruit and vegetables at the market. (a) The mass of fruit and vegetables he sells is in the ratio fruit:vegetables \( =5: 7 \). Hassan sells 1.33 tonnes of vegetables. How many kilograms of fruit does he sell? (b) The amount of money Hassan receives from selling fruit and vegetables is in the ratio fruit: vegetables \( =9: 8 \). Hassan receives a total of \( \$ 765 \) from selling fruit and vegetables. Calculate how much Hassan receives from selling fruit. (c) Calculate the average price of Hassan's fruit, in dollars per kilogr: (d) i) Hassan sells oranges for \( \$ 0.35 \) per kilogram. He reduces this price by \( 40 \% \) ii) The price of \( \$ 0.35 \) per kilogram of oranges is an increase of \( 25 \% \) on the previous day's price. Calculate the previous day's price.

Let's solve each part of the problem step by step. ### (a) The mass of fruit and vegetables is in the ratio \( \text{fruit:vegetables} = 5:7 \). Let the mass of fruit be \( 5x \) and the mass of vegetables be \( 7x \). We know that Hassan sells 1.33 tonnes of vegetables. Since 1 tonne = 1000 kg, we have: \[ 7x = 1.33 \times 1000 = 1330 \text{ kg} \] To find \( x \): \[ x = \frac{1330}{7} = 190 \text{ kg} \] Now, we can find the mass of fruit: \[ \text{Mass of fruit} = 5x = 5 \times 190 = 950 \text{ kg} \] **Answer for (a):** Hassan sells **950 kg** of fruit. ### (b) The amount of money Hassan receives from selling fruit and vegetables is in the ratio \( \text{fruit:vegetables} = 9:8 \). Let the amount received from fruit be \( 9y \) and from vegetables be \( 8y \). The total amount received is: \[ 9y + 8y = 765 \] \[ 17y = 765 \] To find \( y \): \[ y = \frac{765}{17} = 45 \] Now, we can find the amount received from fruit: \[ \text{Amount from fruit} = 9y = 9 \times 45 = 405 \] **Answer for (b):** Hassan receives **$405** from selling fruit. ### (c) To calculate the average price of Hassan's fruit in dollars per kilogram, we need to divide the total amount received from fruit by the mass of fruit sold. We already found: - Amount received from fruit = $405 - Mass of fruit = 950 kg Average price per kilogram: \[ \text{Average price} = \frac{405}{950} \approx 0.4263 \] **Answer for (c):** The average price of Hassan's fruit is approximately **$0.43** per kilogram (rounded to two decimal places). ### (d) i) Hassan sells oranges for \( \$0.35 \) per kilogram and reduces this price by \( 40\% \). To find the new price after the reduction: \[ \text{Reduction} = 0.35 \times 0.40 = 0.14 \] \[ \text{New price} = 0.35 - 0.14 = 0.21 \] **Answer for (d)(i):** The new price of oranges is **$0.21** per kilogram. ii) The price of \( \$0.35 \) per kilogram of oranges is an increase of \( 25\% \) on the previous day's price. Let the previous day's price be \( p \). The equation for the increase is: \[ 0.35 = p + 0.25p = 1.25p \] To find \( p \): \[ p = \frac{0.35}{1.25} = 0.28 \] **Answer for (d)(ii):** The previous day's price was **$0.28** per kilogram.