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# A quart bottle contains a mixture that is 1/3 antifreeze, 2/3 water. A half gallon bottle contains a mixture that is 3/4 antifreeze, 1/4 wat

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A quart bottle contains a mixture that is 1/3 antifreeze, 2/3 water. A half gallon bottle contains a mixture that is 3/4 antifreeze, 1/4 water. The contents of the two bottles are poured into a gallon jug. What is the ratio (one integer to another, in the form a:b) of antifreeze to water in the jug?

Guest May 13, 2015

#2
+82576
+10

1 quart = 1/4 gallon

1/3 of this is antifreeze  = (1/3)(1/4) =  1/12 gallon

And    2/3 is water......so (2/3)(1/4) = 1/6 gallon

And the half-gallon  contains   3/4 antifreeze = (1/2)((3/4) = 3/8 gallon

And the half-gallon  contains (1/4) water =   (1/2)(1/4) = 1/8 gallon

So...the  ratio of antifreeze to water is  [  1/12 + 3/8] / [1/6 + 1/8]  = [11/24] / [14/48] = [22 / 14 ] = [11/ 7] or 11 : 7

CPhill  May 13, 2015
Sort:

#2
+82576
+10

1 quart = 1/4 gallon

1/3 of this is antifreeze  = (1/3)(1/4) =  1/12 gallon

And    2/3 is water......so (2/3)(1/4) = 1/6 gallon

And the half-gallon  contains   3/4 antifreeze = (1/2)((3/4) = 3/8 gallon

And the half-gallon  contains (1/4) water =   (1/2)(1/4) = 1/8 gallon

So...the  ratio of antifreeze to water is  [  1/12 + 3/8] / [1/6 + 1/8]  = [11/24] / [14/48] = [22 / 14 ] = [11/ 7] or 11 : 7

CPhill  May 13, 2015

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