Question

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?

Answer 1

Using two variables
let m be the number of men, ... & w the number of women
\[\Large m+w=102\]
\[\Large 2m-3w=-6\]

Answer 2

i already had an equation written out ; i just don't know what to do from there ..

Answer 3

multiply the first eq by 2

Answer 4

then subtract the second equation

Answer 5

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 ...

Answer 6

Well actually there are to methods,
the use of simultaneous equations that i used above
and using substitution...

Answer 7

Okay well how does the substituion method work ?

Answer 8

*2 methods
Using substitution:
\[\large m+w= 102\]\[\large \implies w=102-m\]

put that in 2nd equation

Answer 9

\[\large 2m-3\left( 102-m \right)=-6\]

Answer 10

Okay ; now i get it ! Thanks (:

Answer 11

\[\large \implies 2m-306+3m=-6\]\[\large \implies 5m=306-6\]\[\large \implies 5m=300\]

Answer 12

\[\Large m=60\]\[\Large w={\large 102-60}=42\]

Using simultaneous equations:\[\large m+w=102\]\[\large \implies 2m+2w=204\]
Subtracting the second equation:\[\Large \begin{matrix}2m+2w=204 \\ 2m-3w=-6 \\ -\ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}\]