Plz me asap plz plz ! i need lots of ! i used 40 points
sarah, john, and david each choose a different favorite positive fraction. each fraction is in simplest form. johns's fraction is a reciprocal of sarah's. david mutiples his fraction by sarah's and finds a product of 12/35. then, he multiplies his fraction by john's number and get a product of 15/7. what is each person's favorite faction? write ur answer in full sentences.
plz

First, some defintions
reciprocals are like a/b and b/a or 5/1 and 1/5

remember,

john's fraction is reciprocal of sarah's
john=a/b
sarah=b/a

david multiplies his by sarah and gets 12/35
(b/a)(david)=12/35

multplies his number by john and gets 12/35
(a/b)(david)=15/7

hmmm

(b/a)(david)=12/35 and
(a/b)(david)=15/7

if we divide them then we do





square root both sides


therefor
b=2 and a=5

john's number is a/b=5/2
sarah's number is 2/5

david, hmm

sarah times david=12/35
2/5 times david=12/35
times both sides by 5/2
david=60/70
david=6/7

check other

john times david=15/7
5/2 times 6/7=15/7
30/14=15/7
15/7=15/7
true

sarah's favorite number is 2/5
john's favorite number is 5/2
david's favorite number is 6/7

21/