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.
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
