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bagirrra123 [75]
3 years ago
11

PLZ HELP ME ASAP PLZ PLZ PLZ!!!!! I NEED LOTS OF HELP!!! I USED 40 POINTS

Mathematics
1 answer:
cupoosta [38]3 years ago
6 0
First, some defintions
reciprocals are like a/b and b/a or 5/1 and 1/5

remember, \frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}

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
\frac{(\frac{b}{a})(david)}{(\frac{a}{b})(david)}=\frac{\frac{12}{35}}{\frac{15}{7}}=
\frac{\frac{b}{a}}{\frac{a}{b}}=\frac{\frac{12}{35}}{\frac{15}{7}}=
(\frac{b}{a})(\frac{b}{a})=(\frac{12}{35})(\frac{7}{15})=
\frac{b^2}{a^2}=\frac{84}{525}=
\frac{b^2}{a^2}=\frac{4}{25}
square root both sides
\frac{b}{a}=\frac{2}{5}

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
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