Question

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?

Answer 1

Answer:

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.