## 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

1. anonymous

@whpalmer4

2. whpalmer4

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

Alana gets 4 out of every 9 candies.

4. whpalmer4

are you sure about that, SZ? :-)

5. SolomonZelman

well, 2:3:4 where Alana gets 4, Joe 3, and John 2....

6. whpalmer4

If john got the fewest candies and Joe got the most...

7. anonymous

7 batches?

8. SolomonZelman

Oh, sorry

9. whpalmer4

John, Alana, and Joe divide the candies into three portions using the extended ratio 2:3:4

10. whpalmer4

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

so she gets 7? or 14?

12. whpalmer4

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

So she gets 3 candies per batch * 7 batch = 21 candies right?

14. anonymous

Yes sorry I am terrible at math!/:

15. whpalmer4

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

oh okay I get what you mean thanks once again your awesome!

17. whpalmer4

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