Explain, how did we split the number in the equation.
How to prove?
Class 10th, Statistics, Rd sharma, Mathematics.
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2. 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.
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Solution:
Given,
John and Jilani together have a total of 45 marbles.
Let John have x marbles.
So, Jivani will have (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.