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A man distributed his computers as follows: a hospital got 1/4 of the total, a school got 1/2 of the remainder and a self help group got 1/3 of what the school got. What remained were 6 more computers than what the self help group got

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Answer:

Originally, there were 48 computers

The hospital got 12.

The school got 18.

The self hep group got 6.

The remainder is 12.

Explanation:

Original number of computers = x

The hospital got x/4. x - x/4 = 3x/4. There were 3x/4 left after the hospital.

The school got 1/2 what was left after the hospital, so the school got

1/2 × 3x/4 = 3x/8

The self help group got 1/3 of what the school got.

1/3 × 3x/8 = 3x/24 = x/8

The remainder is x/8 + 6

x = x/4 + 3x/8 + x/8 + x/8 + 6

The LCD of 4 and 8 is 8. Multiply both sides of the equation by 8 to eliminate all denominators.

8 × x = 8 × x/4 + 8 × 3x/8 + 8× x/8 + 8 × x/8 + 8 × 6

8x = 2x + 3x + x + x + 48

8x = 7x + 48

x = 48

Answer:

Originally, there were 48 computers

The hospital got 12.

The school got 18.

The self hep group got 6.

The remainder is 12.

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