Marble problem and algebra

There are two bags. Each bag contains an unknown number of marbles. If 100 of the marbles in the first bag are placed in the second bag, the number in the second bag is increased by 50%. If 100 of the marbles in the second bag are placed in the first bag, the number in the first bag is increased by 40%. How many marbles are there?

solution

Let y be the number of marbles in the second bag.

Suppose 100 marbles are added to the second bag.

Now there are y + 100 marbles in the second bag.

We also know that y is increased by 50% or y + 0.50y

y + 100 = y + 0.50y

100 = 0.50y

y = 200

There are 200 marbles in the second bag.

Let x be the number of marbles in the first bag.

Suppose 100 marbles are added to the first bag.

Now there are x + 100 marbles in the first bag.

We also know that x is increased by 40% or x + 0.40x

x + 100 = x + 0.40x

100 = 0.40x

x = 250

There are 250 marbles in the first bag.

Therefore, the total number of marbles is x + y = 250 + 200 = 450

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