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anonymous

  • one year ago

A bag contains 63 candies. John, Alana, and Joe divide the candies into three portions using the extended ratio 2:3:4. If john got the fewest candies and Joe got the most, how many candies did Alana get? 1. 7 2. 14 3. 21 4. 28

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  1. anonymous
    • one year ago
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    @whpalmer4

  2. whpalmer4
    • one year ago
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    if we think of this as doling out batches of candy, each batch contains 2+3+4 = 9 pieces, right? How many batches of 9 can we hand out from 63?

  3. SolomonZelman
    • one year ago
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    Alana gets 4 out of every 9 candies.

  4. whpalmer4
    • one year ago
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    are you sure about that, SZ? :-)

  5. SolomonZelman
    • one year ago
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    well, 2:3:4 where Alana gets 4, Joe 3, and John 2....

  6. whpalmer4
    • one year ago
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    If john got the fewest candies and Joe got the most...

  7. anonymous
    • one year ago
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    7 batches?

  8. SolomonZelman
    • one year ago
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    Oh, sorry

  9. whpalmer4
    • one year ago
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    John, Alana, and Joe divide the candies into three portions using the extended ratio 2:3:4

  10. whpalmer4
    • one year ago
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    Yes, 7 batches, and I think we've gotten it nailed down that Alana gets 3 candies from each batch. How many does she get in total?

  11. anonymous
    • one year ago
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    so she gets 7? or 14?

  12. whpalmer4
    • one year ago
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    She gets 3 candies from each batch of 2+3+4 = 9 handed out. You told me that we have enough candies to hand out 7 batches like that.

  13. whpalmer4
    • one year ago
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    So she gets 3 candies per batch * 7 batch = 21 candies right?

  14. anonymous
    • one year ago
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    Yes sorry I am terrible at math!/:

  15. whpalmer4
    • one year ago
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    One of the others gets 2 candies per batch * 7 batches = 14 candies and the guy who gets the most gets 4 candies per batch * 7 batches = 28 candies and if we add them all up, 14 + 21 + 28 = 63 candies (if they didn't add up to the total number, we would know that we made a mistake somewhere)

  16. anonymous
    • one year ago
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    oh okay I get what you mean thanks once again your awesome!

  17. whpalmer4
    • one year ago
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    In general, if you have an extended ratio like \(2:3:4\) or \(a:b:c\), the number given to \(a\) would be \[\frac{a}{a+b+c}*total\] where total is obviously the total number of items similarly \(b\) would get \[\frac{b}{a+b+c}*total\]and if you're thinking \(c\) would get \[\frac{c}{a+b+c}*total\] give yourself a big pat on the back

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