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PLZ HELP ME ASAP PLZ PLZ PLZ!!!!! I NEED LOTS OF HELP!!! 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? Please write ur answer in full sentences.

Plz help me!!
Thanks!!

Respuesta :

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

remember, [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}[/tex]

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

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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