5lb, chap 21, # 32

[anik1989]

the explanation shows average of the percent in each case. but i can not understand why average should be done??
please sir,kindly explain my question

[tommywallach]

Hey Anik,

I'm not totally sure I understand your question. This is a weighted average question in the averages chapter, so that's the method at issue.

With the first box, the average of fine and dandy (6%) and Monster Smash (12%) would be 9%. So if we had an equal amount of F&D and MS, the result would be 9% alcohol. But we've been told we will have MORE MS than F&D, and that means we will have a total alcohol content that is more than 9%. If it helps, imagine we have 100 grams of F&D, so 6 grams of alcohol, and 200 grams of MS, so 24 grams of alcohol. This would add up to 30 grams of alcohol out of 300 total grams, which is 10% alcohol

For the second box, the 11.5 is just a distraction. This question is just about what happens when we have the SAME amount of each liquor, so we can just take the average of 4, 6, and 12. If it helps, imagine we had 100 grams of each liquor. DF would thus have 4 grams of alcohol, F&D would have 6 grams, and MS would have 12 grams. Our final total would be 22 grams of 300 grams total, which is more than 7%.

For the third box, we can average DF, two F&Ds, and a zero term, or use our placeholder numbers again. 100 grams of DF is 4 grams of alcohol. 200 grams of F&D is 24 grams of alcohol. And then 100 grams of alcohol free mixer. This means we have 28 grams of alcohol for 400 grams of drink, which is EXACTLY 7% alcohol (but not MORE than 7%).

-t

[anik1989]

thank sir, for your kind time

[anik1989]

i wanted this type of explanation, thank you very much sir

[tommywallach]

Glad to do it, Anik! I know I give you a hard time now and then, but I really am here to help! : )

-t