Example 1 (i) - Chapter 4 Class 10 Quadratic Equations

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Example 1 Represent the following situations mathematically: (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. Total number of marbles = 45 Let the number of marbles with John = x So, number of marbles with Jivanti = 45 – x marbles After losing 5 marbles, Number of marbles with John = x – 5 Number of marbles with Jivanti = 45 – x – 5 = 40 – x Given that Product of marbles now = 124 (x – 5) (40 – x) = 124 x (40 – x) – 5 (40 – x) = 124 40x – x2 – 200 + 5x = 124 45x – x2 – 200 = 124 0 = x2 + 200 – 45x + 124 0 = x2 – 45x + 324 x2 – 45x + 324 = 0 Hence, the required quadratic equation is x2 – 45x + 324 = 0