David had 2 bags of marbles. After he had sold 44 marbles from Bag X to his friend, the number of marbles in Bag Y was 5/7 of the number of marbles in Bag X. Given that there were 2/5 as many marbles in Bag Y as in Bag X originally, find the number of marbles in Bag X at first.

Answers (1)

Let Number of marbles in bag X $$ = x $$

and number of marbles in Bag Y $$ = y $$

According to the question,

                                      $$ y = frac25 x $$

After David sold 44 marbles in Bag  X  = $$x - 44$$

Now,  

                                                $$ y=frac57 (x - 44) $$

put the value

                                 $$ y = frac25 x $$ in the above equation

we get

                                $$frac25 x =frac57 (x-44)$$ \$$ $$ frac25x= frac57x - frac5	imes 447$$$$

cross multiplication, 

                         $$25x - frac14x5	imes 7 = frac2207$$\$$ $$frac11x35 = frac2207$$\$$ $$ 11x = frac35	imes 2207 $$\$$ $$ 11x = 5	imes 220$$\$$ $$ x = 5 	imes 20 $$\$$ $$ x = 100 $$

Hence, the marbles numbers = 100 

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