Question

John and janvi together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they now have, is 124. Find out how many marbles they had to start with?

Answer 1

Answer:

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 =124

∴(x−5)(40−x)=124

40x−x²−200+5x=124

−x²+45x−200−124=0

x²−45x+328=0 --- (Multiplying by(-1))

By factorization method

x

2

−36x−9x+324=0

x(x−36)−9(x−36)=0

(x−36)(x−9)=0

x=36 or x=9

When John has 36 Marbles, Jivanti has =45−x=45−36=9 marbles

When John has 9 Marbles and Jivanti has =45−x=45−9=36 marbles

Step-by-step explanation:

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Answer 2

$\boxed{ \boxed{ \bf \dag \: Note : - }}$

Here, we have to find the number of marbles, so we assume that one of them (John or Janvi) has x marbles and then apply all the conditions to get required quadratic equation.

$\boxed{ \boxed{ \bf \: SOLUTION}}$

Given, John and Janvi together have 45 marbles.

Let John has x marbles.

Then, number of marbles Janvi had = 45 – x

$\because \: \rm \: Both \: of \: them \: lost \: 5 \: marbles \: each.$

$\therefore \: \rm \: The \: number \: of \: marbles \: John \: had = x - 5$

and the number of marbles Janvi had = 45 – x – 5 = 40 – x

Now, product of the number of marbles = 124

$\therefore \: \rm \: \: \: \: \: \: \: \: \: \: (x - 5)(40 - x)= 124$

$\implies \: \: \rm \: 40 x - {x}^{2} - 200 + 5x = 124$

$\implies \: \rm \: - {x}^{2} + 45x - 200 - 124 = 0$

$\implies \: \rm \: - {x}^{2} + 45x - 324 = 0$

$\implies \: \rm \: {x}^{2} - 45x + 324 = 0 \: \: \: \: \: \: \: [multiplying \: by \: ( - 1)]$

which is the required quadratic equation.

Now, by factorisation method, we get

$\rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: x {}^{2} - 36x - 9x + 324 = 0$

$\implies \: \rm \: x(x - 36) - 9(x - 36) = 0$

$\implies \: \rm \: (x - 36)(x - 9) = 0$

$\implies \: \rm \: x - 36 = 0 \: or \: x - 9 = 0$

$\implies \: \rm \: x = 36 \: or \: x = 9$

when John has 36 marbles, then Janvi has

$\rm \: \: \: \: \: \: \: = 45 - 36 = 9 \: marbles.$

when John has 9 marbles then Janvi has

$\rm \: \: \: \: \: \: \: = 45 - 9 = 36 \: marbles.$