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 and x marbles.

Answer 1

SOLUTION :

Given : John and jivanti together have 45 marbles

Let the number of Marbles John had be= x

Then the number of marbles jivanti had= (45 - x)

Both of them lost 5 Marbles each

Therefore, the number of marbles John had = (x - 5)

The number of marbles jivanti had = 45 - x - 5 = (40 - x)

Now product of the number of Marbles = 128

Therefore , (x - 5)(40 - x) = 128

40 -  x² - 200 + 5x = 128

-x² + 45x - 200 - 128 = 0

x² - 45x + 328 = 0        [Multiplying by(-1)]

Hence, the required quadratic equation is x² - 45x + 328 = 0 .

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Answer 2

I have explained the answer below!

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Thank you !

John and jivanti together have 45 marbles

Let the number of Marbles John had be= x

Then the number of marbles jivanti had= (45 - x)

Both of them lost 5 Marbles each

Therefore, the number of marbles John had = (x - 5)

The number of marbles jivanti had = 45 - x - 5 = (40 - x)

Now product of the number of Marbles = 128

Therefore , (x - 5)(40 - x) = 128

40 -  x² - 200 + 5x = 128

-x² + 45x - 200 - 128 = 0

x² - 45x + 328 = 0        [Multiplying by(-1)]

Hence, the required quadratic equation is x² - 45x + 328 = 0 .