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  • 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)



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