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On a recent trip to the convenience store, you picked up 3 gallons of milk, 6 bottles of water, and 6 snack-size bags of chips. Your total bill (before tax) was $29.10. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.70 more than a bottle of water, how much does each item cost?

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Hi

the trick is to define price by referring only to one item.  

Here the bootle of water is you reference.  

there is 3 gallons  of milk

             6 bottles of water

              6 bags of chips

let's call bottle of water  " X"  

water cost  = X

milk = X+1.7

chips =  X/2

So we have  :  

3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1

3X+ 5.1 + 6X + 6X/2 = 29.1

3X +6X + 3X + 5.1 = 29.1

 12X +5.1 = 29.1

  12X = 29.1 - 5.1

   12 X =  24

        X = 24/12

        X = 2

price of bottle is  2 dollars  

then milk is  2 + 1.7 = 3.7

        chips =  2/2 = 1

let's check =  3*3.7 + 6*2 + 6*1 =   11.1+12+ 6 = 29.1

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