Levi organized 45 shirts into 3 drawers. molly came and rearranged the shirts. she moved 6 shirts from the top drawer to the middle drawer, then she move 4 shirts from the middle drawer to the bottom drawer, then she moved 5 shirts from the the bottom drawer to the top drawer. now each drawer has the same amount of shirts. how many shirts were there before molly came?

There were 16, 13 and 16 in first, second and third drawer respectively.

Explanation:

Given,

Total number of shirts = 45,

Number of drawers = 3,

Let x, y and z be the number in first, second and third drawer respectively,

After moving 6 shirts from the top drawer to the middle drawer,

Shirts in,

First drawer = x - 6

Second drawer = y + 6

Third drawer = z,

After moving 4 shirts from the middle drawer to the bottom drawer,

First drawer = x - 6

Second drawer = y + 6 - 4 = y + 2

Third drawer = z + 4,

Finally, after moving 5 shirts from the bottom drawer to the top drawer,

First drawer = x - 6 + 5 = x - 1,

Second drawer = y + 2

Third drawer = z + 4 - 5 = z - 1

According to the question,

x - 1 = y + 2 = z - 1

⇒ x - 1 = z - 1

⇒ x = z (1)

Also,  x - 1 = y + 2

⇒ y = x - 1 - 2 = x - 3 (2)

Since, total shirts = 45

⇒ x + y + z = 45

From equation (1) and (2),

x + x - 3 + x = 45

⇒ 3x -3 = 45

⇒ 3x = 48

⇒ x = 16,

Again from equation (1) and (2),

z = 16 and y = 16 - 3 = 13

Hence, there were 16, 13 and 16 in first, second and third drawer respectively.

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