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An ammonia and water mixture fills a five-gallon container. Eighty percent of the mixture is ammonia but some of the mixture will be drained and replaced with pure water. If a five gallon mixture of sixty percent ammonia is desired, how many quarts of the mixture need to be drained before the water is added? (A quart is onefourth of a gallon.)

 Jun 29, 2022
 #1
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4 galllons of the current  mixture is  ammonia  (80% of 5)

We need 3 gallons of ammonia at the  end

Let x be the number of gallons drained off and.8x the amount of  ammonia drained off

 

(4 - .8x) = .6 *5

 

4 - .8x  = 3

 

4 - 3  =  .8x

 

1 = .8x

 

1/.8  = x = 1.25

 

We need to drian off  1.25 gal

 

Proof

 

4 gallons of  ammmonia to start with

When we drain away 1.25  gallons, 80%  of this is ammonia.....so   4 - .8(1.25)  = 3 gallons of ammonia are left

Adding back 1.25 gallons  of  pure water  = 5 gallons  and 3 of  this is  ammonia...so....3/5=  .60  =  60% 

 

And 1.25 gallons =     5 qts

 

 

cool cool cool

 Jun 29, 2022

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