how many penny rolls does Hannah have?

Question

Hannah is putting her loose change into rolls by denomination. Most of her rolls are penny rolls.  There are 4/5 as many dime rolls as penny rolls. There are 3/10 as many quarter rolls as dime rolls. If there are 15 quarter rolls, how many penny rolls does Hannah have?

Answer 1

Here's what we know:

d = 4/5 p (if she has 5 penny rolls, there will be 4 dime rolls)

q = 3/10 d (if she has 10 dime rolls, there will be 3 quarter rolls)

q = 15

 

15 = 3/10 d

150 = 3d

50 = d

 

50 = 4/5 p

250 = 4p

62.5 = p

 

So Hannah has 62 completed rolls and another half-full.

 

Answer 2

Let x = penny rolls

 

dime rolls = 4/5 X

 

quarter rolls = 3/10 dime rolls = (3/10)(4/5) X = 15

 

Now you can backout X as

 

X = 15 (5/4)(10/3) = 750/12 = 62 1/2 penny rolls (is half a roll allowed?)

 

But the answer checks out.