jonh and jivanti together have 45 marbles.both of them lost 5 marble each and the product of the number of marbles they now have is 124 .from the quadratic equation to find how many marbles they had to start with,if John had X marble
Answers
Given:-
- jonh and jivanti together have 45 marbles.both of them lost 5 marble.
- The product of the number of marbles they now have is 124 .
To find:-
- Find how many marbles had to start John had X marble.
Solutions:-
Let the number of john's marbles be x.
Therefore, number of jivanti's marble = 45 - x
After losing 5 marble,
Number of john's marbles = x - 5
Number of jivanti's marbles = 45 - x - 5 = 40 - x
The product of the number of marbles is 124.
Therefore,
=> (x - 5) (40 - x) = 124
=> 40x - x² - 200 + 5x = 124
=> x² - 45x + 200 = - 124
=> x² - 45x + 324 = 0
=> x² - 36x - 9x + 324 = 0
=> x(x - 36) - 9(x - 36) = 0
=> (x - 36) (x -9)
=> x - 36 = 0 or x - 9 = 0
=> x = 36 or x = 9
The number of john's marbles = 36
Thus, the number of jivanti's marbles = 45 - 36 = 9
Number of john's marbles = 9
Thus, number of jivanti's marbles = 45 - 9 = 36.
Answer:
Let the number of john's marbles be x.
Therefore, number of jivanti's marble = 45 - x
After losing 5 marble,
Number of john's marbles = x - 5
Number of jivanti's marbles = 45 - x - 5 = 40 - x
The product of the number of marbles is 124.
Therefore,
=> (x - 5) (40 - x) = 124
=> 40x - x² - 200 + 5x = 124
=> x² - 45x + 200 = - 124
=> x² - 45x + 324 = 0
=> x² - 36x - 9x + 324 = 0
=> x(x - 36) - 9(x - 36) = 0
=> (x - 36) (x -9)
=> x - 36 = 0 or x - 9 = 0
=> x = 36 or x = 9
The number of john's marbles = 36
Thus, the number of jivanti's marbles = 45 - 36 = 9
Number of john's marbles = 9
Thus, number of jivanti's marbles = 45 - 9 = 36.
Step-by-step explanation: