Question

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 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.

Answer 1

Let the number of John's marbles be x.

Therefore, number of Jivanti's marble = 45 - x

After losing 5 marbles,

Number of John's marbles = x - 5

Number of Jivanti's marbles = 45 - x - 5 = 40 - x

It is given that the product of their marbles is 128.

∴ (x - 5)(40 - x) = 128

⇒ 40x - x² – 200 + 5x = 128

⇒ 45x - x² – 200 - 128 = 0

⇒ 45x - x² - 328 = 0

⇒ -(x² - 45 + 328) = 0

⇒ x² - 45 + 328 = 0

∴ The required quadratic equation is x² - 45 + 328 = 0