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

Do the math. she originally had 50 dollars on her gift card and she had 12 dollars left on her gift card after she finished her shopping spree. if you subtract 50 minus 12 you get thirty eight dollars as your answer. so therefore, ciara spent 38 dollars total o