Multiple choice

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 $124$. From the quadratic equation to find how many marbles they had to start with, if John had $x$ marbles.

  1. $36,9$
  2. $20,25$
  3. $30,15$
  4. $27, 18$
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A Correct answer
Explanation

Let John have x, Jivanti have 45-x. After losing 5, John has x-5, Jivanti has 40-x. (x-5)(40-x) = 124 => 40x - x^2 - 200 + 5x = 124 => x^2 - 45x + 324 = 0. Factors are (x-36)(x-9) = 0. So x = 36 or 9.

AI explanation

Since the total is 45 marbles and John has x marbles, Jivanti has (45 - x) marbles. After both lose 5 marbles, John has (x - 5) and Jivanti has (40 - x) marbles; setting their product to 124 gives the equation (x - 5)(40 - x) = 124, which simplifies to x^2 - 45x + 324 = 0. Solving this quadratic equation yields x = 36 or x = 9, meaning the initial marble counts were 36 and 9.

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