Question

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

john have marbles is 45.
and jivanti have marbles is 45.
= 45+45
= 90 marbles
the lost marbles is 5.
= 90-5 marbles
= 85 marbles.
the product of the number of marbles is 124.
= 124-85 marbles
= 39 marbles
hence, the marbles the had to start with is 39 marbles.

Answer 2

$\huge\sf\star{\green{\underline{\underline{\mathcal{Explanation:}}}}}$

______________________________

Given that:-

• 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.

To find:-

• How many marbles they had to start with?

______________________________

Let ,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

$\bold\hookrightarrow$Given that the product of their marbles is 124.

∴ (x – 5)(40 – x) = 124

$\bold\hookrightarrow$ x^2 – 45x + 324 = 0

$\bold\hookrightarrow$x^2 – 36x – 9x + 324 = 0

$\bold\hookrightarrow$x(x – 36) -9(x – 36) = 0

$\bold\hookrightarrow$(x – 36)(x – 9) = 0

Thus, we can say,

x – 36 = 0 or x – 9 = 0

$\bold\leadsto$x = 36 or x = 9

Therefore,

If, John’s marbles = 36,

Then, Jivanti’s marbles = $\star\boxed{45-36=9}$

And if John’s marbles = 9,

Then, Jivanti’s marbles = $\star\boxed{45-9=36}$

$\huge\star{\blue{\underline{\mathscr{Hence,Solved!}}}}$