Question

The ratio of the number of oranges to the number of pears at a fruit stall in the beginning was 5:9. After 25 pears were sold, the ratio of the number of oranges to the number of pears became 10: 13. Find the number of pears left at the fruit stall in the end.​

Answer 1

Let's use algebra to solve this problem.Let's represent the initial number of oranges and pears as 5x and 9x, respectively, where x is a constant.After 25 pears were sold, the new number of pears became 9x - 25, and the ratio of oranges to pears became 10:13. This means that the new number of oranges is 10/13 of the new number of pears.So we can set up the following equation:10/13 * (9x - 25) = 5xMultiplying both sides by 13 to eliminate the fraction, we get:10(9x - 25) = 65xExpanding the brackets, we get:90x - 250 = 65xSubtracting 65x from both sides, we get:25x - 250 = 0Adding 250 to both sides, we get:25x = 250Dividing both sides by 25, we get:x = 10So the initial number of oranges is 5x = 50, and the initial number of pears is 9x = 90.After 25 pears were sold, the new number of pears is 9x - 25 = 65, and the new number of oranges is 10/13 * 65 ≈ 50.Therefore, the number of pears left at the fruit stall in the end is 65.