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2 answers:
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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
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