Question

John and Jivani 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 to start with, if John had x marbles.

Answer 1

Given,

John and Jilani together have a total of 45 marbles.

Let John have x marbles.

So, Jivani will be having (45 – x) marbles.

Number of marbles John had after losing 5 marbles = x – 5

Number of marbles Jivani had after losing 5 marbles = (45 – x) – 5 = 40 – x

Now, according to the question the product of the marbles that they are having now is 128

So,

(x – 5)(40 – x) = 128

⇒ 40x – x² – 200 = 128

⇒ x² – 45x + 128 + 200 = 0

⇒ x² – 45x + 328 = 0

Thus the required quadratic equation is x² – 45x + 328 = 0.