John and Jivanti together have 45 marbles. Both of them lost 5 marbles

1.	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» Number of marbles John has is x. Given, John and Jivanti together have 45 marbles. Number of marbles which Jivanti has = 45 – x Now, both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. So John will have x - 5 marbles and Jivanti will have 45 - x - 5 = 40 - x marbles. ⇒ (x – 5)(40 – x) = 128 ⇒ 40x – 200 + 5x – x² = 128 ⇒ 40x – 200 + 5x – x² - 128 = 0 ⇒ 45x – 328 – x² = 0 ⇒ x²– 45x + 328 = 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 128. Form the quadratic equation to find how many marbles they had to start with, if john had x marbles.

Answer»

Number of marbles John has is x.

Given, John and Jivanti together have 45 marbles.

Number of marbles which Jivanti has = 45 – x

Now, both of them lost 5 marbles each, and the product of the number of marbles they now have is 128.

So John will have x - 5 marbles and Jivanti will have 45 - x - 5 = 40 - x marbles.

⇒ (x – 5)(40 – x) = 128

⇒ 40x – 200 + 5x – x² = 128

⇒ 40x – 200 + 5x – x² - 128 = 0

⇒ 45x – 328 – x² = 0

⇒ x²– 45x + 328 = 0