Question

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

Answer 1

@whpalmer4

Answer 2

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?

Answer 3

Alana gets 4 out of every 9 candies.

Answer 4

are you sure about that, SZ? :-)

Answer 5

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

Answer 6

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

Answer 7

7 batches?

Answer 8

Oh, sorry

Answer 9

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

Answer 10

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?

Answer 11

so she gets 7? or 14?

Answer 12

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.

Answer 13

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

Answer 14

Yes sorry I am terrible at math!/:

Answer 15

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)

Answer 16

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

Answer 17

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