Question

Represent the following situations mathematically:
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 124. We would like to find out how many marbles they had to start with.

Answer 1

Answer:

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Let us take that John has x marbles and Jhanvi has y marbles.

According to the conditions ;

x + y = 45

x = 45 - y ----(1)

After losing 5 marbles each

( x - 5 ) ( y - 5 ) = 124 ----(2)

substituting eq (1) in eq (2)

(45 - y -5 ) ( y - 5 ) = 124

(50-y)(y-5) = 124

50y -y^2 - 250 - 5y = 124

y^2 - 50y+ 5y + 250 +124 =0

y^2 -45y + 324 = 0

y^2 -9y-36y+324 =0

y(y -9 )-36(y-9)=0

y = 36 and y = 9

case 1

y = 36

x = 45 - 36

x = 9

case2

y = 9

x= 45 - 9

x = 36

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Answer 2

(i) Let us say, the number of marbles John have = x.

Therefore, number of marble Jivanti have = 45 – x

After losing 5 marbles each,

Number of marbles John have = x – 5

Number of marble Jivanti have = 45 – x – 5 = 40 – x

Given that the product of their marbles is 124.

∴ (x – 5)(40 – x) = 124

⇒ x2 – 45x + 324 = 0

⇒ x2 – 36x – 9x + 324 = 0  

⇒ x(x – 36) -9(x – 36) = 0

⇒ (x – 36)(x – 9) = 0

Thus, we can say,

x – 36 = 0 or x – 9 = 0

⇒ x = 36 or x = 9

Therefore,  

If, John’s marbles = 36,

Then, Jivanti’s marbles = 45 – 36 = 9

And if John’s marbles = 9,

Then, Jivanti’s marbles = 45 – 9 = 36