Ayana and Helix had 45 marbles. Both of them lost 5 marbles each. The product of the marbles they now have is 174. Ayana had fewer marbles
than Helix. How many marbles did Ayana start with

Let the no. of marbles john had be x

Then the no. of marbles jivanti had = (45-x)

The no. of marbles left with john, when he lost 5 marbles = 45-x-5=40 - x

Therefore their product = (x-5)(40-x)

=40x - x2 -200+5x

=x2+45x-200

So,-x2 + 45x-200=124. (given , product =124)

so, x2-45x+324=0

Therefore, the no. of marbles john had , satisfies the quadratic eqn ,

x2-45x+324.

When u will find the value x of this eqn that no. will be the no. of marbles they started with!

Hope it helps

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