The ratios of punch mix to water for several fruit drinks are given. punch mix mix water grape 1 cup 3 cups cherry 5 cups 12 cups lemon 7 cups 12 cups orange 2 cups 3 cups which flavor has the smallest ratio of mix to water?

Step-by-step explanation:

We have been given the ratios of punch mix to water for several fruit drinks as : Grape mix (1 cups to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups) and Orange mix (2 cups to 3 cups).

To find which flavor has the smallest ratio of mix to water let us compare all the given proportions by having a common base.  

Now let us have a common denominator 12 as LCM of 3 and 12 is 12.  

We can see that grape mix has the smallest proportion of mix to water, therefore, grape mix will be the correct choice.

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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