Gail washed 1/6 of a stack of dishes, and Andrew washed 1/2 of the remaining dishes. 45 dishes remain. How many dishes were there before Gail and Andrew started washing them?

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by Chesnut

Answers

• Brainly User
2016-03-21T21:38:15+08:00

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Let x be the original number of dishes.
Gail washed 1/6 (x)
Remaining dishes: 6/6 - 1/6 = 5/6

Andrew washed 1/2 of the remaining dishes:
(1/2)(5/6)(x) = 5/12 (x)

Remaining dishes after Andrew and Gail washed some stack of dishes:
45 dishes

Equation:
(1/6) (x) + (5/12)(x) + 45 = x

Multiply each term by LCD 12:
(12)(1/6)(x) + (12)(5/12)(x) + (12)(45) = (12)(x)
2x + 5x + 540 = 12x
7x + 540 = 12x
12x - 7x = 540
5x = 540
5x/5 = 540/5
x = 108

ANSWER:  There were 108 dishes before Gail and Andrew started washing them.

Check:
Gail washed 1/6 of 108 = 18 dishes
108 - 18 = 90 dishes

Andrew washed 1/2  of the remaining 90 dishes = 45 dishes

Remaining dishes after Gail and Andrew washed some of the them = 45 dishes.

Add:
18 + 45 + 45 = 108
108 = 108 (true)