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Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to 6, how many women auditioned?
 2 years ago
 2 years ago
Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to 6, how many women auditioned?
 2 years ago
 2 years ago

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PaxPolarisBest ResponseYou've already chosen the best response.2
Using two variables let m be the number of men, ... & w the number of women \[\Large m+w=102\] \[\Large 2m3w=6\]
 2 years ago

bprice26Best ResponseYou've already chosen the best response.0
i already had an equation written out ; i just don't know what to do from there ..
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
multiply the first eq by 2
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
then subtract the second equation
 2 years ago

bprice26Best ResponseYou've already chosen the best response.0
What ? How would i do that .. Do i multiply 102 by 2 ??? I am soooo confused , i have been reading all my lessons and doing all my work i just don't get it, it makes no sense to me ...
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
Well actually there are to methods, the use of simultaneous equations that i used above and using substitution...
 2 years ago

bprice26Best ResponseYou've already chosen the best response.0
Okay well how does the substituion method work ?
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
*2 methods Using substitution: \[\large m+w= 102\]\[\large \implies w=102m\] put that in 2nd equation
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
\[\large 2m3\left( 102m \right)=6\]
 2 years ago

bprice26Best ResponseYou've already chosen the best response.0
Okay ; now i get it ! Thanks (:
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
\[\large \implies 2m306+3m=6\]\[\large \implies 5m=3066\]\[\large \implies 5m=300\]
 2 years ago

PaxPolarisBest ResponseYou've already chosen the best response.2
\[\Large m=60\]\[\Large w={\large 10260}=42\] Using simultaneous equations:\[\large m+w=102\]\[\large \implies 2m+2w=204\] Subtracting the second equation:\[\Large \begin{matrix}2m+2w=204 \\ 2m3w=6 \\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}\]
 2 years ago
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