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Let the number of marbles John had = x Then, the number of marbles Jivanti had = (45 – x). According to the given question, (x – 5) (45 – x – 5) = 124 ⇒ (x – 5) (40 – x) – 124 = 0 ⇒ 40x – x 2 – 200 + 5x– 124 =0 ⇒ –x 2 + 45x – 324 =0 ⇒ x 2 – 45x + 324 = 0 x 2 – 36x – 9x + 324 = 0 ⇒ x(x – 36) – 9(x – 36) = 0 ⇒ (x – 36) (x – 9) = 0 x – 36 = 0 or x – 9 = 0 x = 36 or x = 9 Hence, the number of marbles John had = 36 and the number of marbles Jivanti had = 45 - 36 = 9.

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Quadratic Equations

Long Answer Type

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Short Answer Type

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Long Answer Type

18. 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.

Let the number of marbles John had = x Then, the number of marbles Jivanti had = (45 – x).
According to the given question,
(x – 5) (45 – x – 5) = 124
⇒ (x – 5) (40 – x) – 124 = 0
⇒ 40x – x² – 200 + 5x– 124 =0
⇒ –x² + 45x – 324 =0
⇒ x² – 45x + 324 = 0
x² – 36x – 9x + 324 = 0
⇒ x(x – 36) – 9(x – 36) = 0
⇒ (x – 36) (x – 9) = 0
x – 36 = 0 or x – 9 = 0
x = 36 or x = 9
Hence, the number of marbles John had = 36 and the number of marbles Jivanti had = 45 - 36 = 9.

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