# 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,

$y = \frac{2}{5} x$

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

Now,

$y=\frac{5}{7} (x - 44)$

put the value

$y = \frac{2}{5} x$ in the above equation

we get

$\frac{2}{5} x =\frac{5}{7} (x-44) \\ \frac{2}{5}x= \frac{5}{7}x - \frac{5\times 44}{7}$

cross multiplication,

$25x - \frac{14x}{5\times 7} = \frac{220}{7}\\ \frac{11x}{35} = \frac{220}{7}\\ 11x = \frac{35\times 220}{7} \\ 11x = 5\times 220\\ x = 5 \times 20 \\ x = 100$

Hence, the marbles numbers = 100

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