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Quadratic Equations
Question
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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.

Answer

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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Some More Questions From Quadratic Equations Chapter

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x2 – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x2 + x – 6 = 0

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.

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