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anonymous

  • one year ago

In a group of 50 patrons, 12 patrons like lattes and espressos, 9 patrons like espressos and cappuccinos, 8 patrons like lattes and cappuccinos, and 4 patrons like all 3 coffee drinks. Altogether, 20 patrons like lattes, 22 patrons like espressos, and 17 patrons like cappuccinos. How many patrons don't like any of these coffee drinks? A. 18 B. 14 C. 12 D. 16

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  1. mathmate
    • one year ago
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    Are you familiar with Venn diagrams?

  2. anonymous
    • one year ago
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    yes a little

  3. mathmate
    • one year ago
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    I'll start the diagram, and we will work together to fill the numbers, is that ok for you?

  4. anonymous
    • one year ago
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    ya

  5. mathmate
    • one year ago
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    |dw:1436841362792:dw|

  6. mathmate
    • one year ago
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    ok, now it's your turn to put in as many numbers as you can from the given question. You can proceed.

  7. mathmate
    • one year ago
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    If you have doubts, just ask.

  8. mathmate
    • one year ago
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    I'll give you a hint by putting in: "4 patrons like all three coffee drinks" in the middle. |dw:1436841764504:dw| Does that help?

  9. mathmate
    • one year ago
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    You will notice that the "4" is placed in a location which is inside all three circles. Each circle represents a coffee drink. So being inside all circles mean symbolically that 4 patrons like all three drinks. You can choose other locations to indicate the number of patrons who like certain combination of drinks.

  10. mathmate
    • one year ago
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    @hau.li are you still there?

  11. anonymous
    • one year ago
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    yes aha

  12. mathmate
    • one year ago
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    Would you like to fill in some numbers?

  13. anonymous
    • one year ago
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    how do i show you what i have?

  14. mathmate
    • one year ago
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    you can click on the button with a pencil at the top of the picture and fill the numbers using the drawing tool.

  15. anonymous
    • one year ago
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    |dw:1436842250565:dw|

  16. anonymous
    • one year ago
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    correct?

  17. anonymous
    • one year ago
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    ?

  18. anonymous
    • one year ago
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    is the answer B

  19. mathmate
    • one year ago
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    The 4 in the middle is correct, and should stay, as I have indicated how it was put in. The 12 includes the 4, so shoul be changed to the 8, same has to be adjusted for all numbers shown. If you want to check answers, I suggest you give me the answer value, not the choice letter, to avoid confusion. Also, I would like to know how you get the answer when the total number of patrons exceed 50.

  20. anonymous
    • one year ago
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    is the answer 14?

  21. misty1212
    • one year ago
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    |dw:1436843495272:dw| how many like lattes and espresso?

  22. anonymous
    • one year ago
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    12

  23. anonymous
    • one year ago
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    is the answer 14?

  24. anonymous
    • one year ago
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    hello

  25. mathmate
    • one year ago
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    This was a response written when there was an interruption in my connection. Not quite, you may not have understood the concept of the Venn diagram. Each of the 50 patrons has one single place in the diagram, i.e. inside one circle (means he likes only one drink), inside two (means he likes exactly 2 drinks), or inside all three (means he likes all three drinks). the 12 the question gives is intended to mean at least two drinks, latte and expresso. Actually we know that 4 drinks all three, so there are only 8 who like JUST latte and expresso. The total is still 12 (8+4). So if you fix all the numbers this way, the total of the numbers will tell you the number of patrons who drink at least one coffee drink. Take the total from 50 (total number of patrons), you will get the number of patrons who don't drink any coffee drink. Try that out and post your new calculations.

  26. anonymous
    • one year ago
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    16?

  27. mathmate
    • one year ago
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    |dw:1436877904934:dw| Continue filling the numbers and you will be able to confirm or correct your answer.

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