What Proportion of his collection must S give away for two sets to be equal?

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addmmm

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The number of pens in J's pen collection equals 5/8 the number of pens in S's collection.

What proportion of his own collection must S give to J in order for both of them to
have the same number of pens?
 
Last edited:
addmmm said:
The number of pens in J's pen collection equals 5/8 the number of pens in S's collection.

What proportion of his own collection must S give to J in order for both of them to
have the same number of pens?
Click to expand...
???? What have you tried? No one from the forum, freemathHELP, can help you if you do not state where you are getting stuck.
I'll provide a hint. What proportion will s give to j if they have a total of 13 pens? 26 pens? 39 pens?
 
Last edited:
addmmm said:
The number of pens in J's pen collection equals 5/8 the number of pens in S's collection.

What proportion of his own collection must S give to J in order for both of them to
have the same number of pens?
Click to expand...

Suppose S had 16 pens. How many pens does J have? How many pens must S give to J so they have the same number of pens? What percent of S's original collection is that?
 
addmmm said:
The number of pens in J's pen collection equals 5/8 the number of pens in S's collection.
Click to expand...
So draw a bar with eight boxes for S's pens, and five boxes for J's pens:

Code: 
pens:
   +-+-+-+-+-+-+-+-+
S: | | | | | | | | |
   | | | | | | | | |
   | | | | | | | | |
   +-+-+-+-+-+-+-+-+
   |         |
   +-+-+-+-+-+
J: | | | | | |
   | | | | | |
   | | | | | |
   +-+-+-+-+-+

addmmm said:
What proportion of his own collection must S give to J in order for both of them to have the same number of pens?
Click to expand...
How much of those excess three boxes of S's would you need to split off to give to J, for them to have the same amount of pens?

If you split each of the original boxes into two, what fractional portion does this give you?

Code: 
pens:
   +-+-+-+-+-+-+-+-+
S: | | | | | | | | |
   +-+-+-+-+-+-+-+-+
   | | | | | | | | |
   +-+-+-+-+-+-+-+-+
   |         |
   +-+-+-+-+-+
J: | | | | | |
   +-+-+-+-+-+
   | | | | | |
   +-+-+-+-+-+
If you get stuck, please write back showing what you've tried so far. Thank you! ;)
 
Got it guys, sorry; don't know why it took so long:

original: J = (5/8)S ;
n=#pens Simon gives away, so

J+ n = S - n --> (5/8)S + n = S - n --> 2n = S(1- 5/8) =(3/8)S

n = (3/16)S
 
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