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.
Answers
no. of marbles with john is 36 or 9
no. of marbles with jivanti is 9 or 36 respectively
•let the no. of marbles with john is x
=> no. of marbles with jivanti is 45-x
• If they both lost 5 marbles
=>no. of marbles with john is x-5
& no. of marbles with jivanti is 40-x
• According to question
(x-5)(40-x) = 124
=>40x-x²-200+5x=124
=>x²-45x+324 =0
=>x²-36x-9x+324=0
=>x(x-36)-9(x-36)=0
=>(x-36)(x-9)=0
=>x=36 or x=9
No. of marbles with John is 36 or 9 No. of marbles with Jivanti is 9 or 36
Given:
- John and Jivanti together have 45 marbles.
- Both of them lost 5 marbles each.
- The product of the number of marbles they now have is 128.
To find:
How many marbles they had to start.
Explanation:
- Consider John had x marbles.
- No. of marbles with Jivanti is 45-x
- If they both lost 5 marbles
- No. of marbles with John is x-5
- And No. of marbles with Jivanti is 40-x
- According to question
(x-5)(40-x) = 128
40x -x² -200 + 5x = 128
x²-45x+328 = 0
x²-36x - 9x + 328 = 0
x (x-36) - 9 (x-36) = 0
(x-36)(x-9) = 0
x = 36 or x = 9
No. of marbles with John is 36 or 9
No. of marbles with Jivanti is 9 or 36
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