## bprice26 3 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?

1. PaxPolaris

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

2. bprice26

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

3. PaxPolaris

multiply the first eq by 2

4. PaxPolaris

then subtract the second equation

5. bprice26

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 ...

6. PaxPolaris

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

7. bprice26

Okay well how does the substituion method work ?

8. PaxPolaris

*2 methods Using substitution: $\large m+w= 102$$\large \implies w=102-m$ put that in 2nd equation

9. PaxPolaris

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

10. bprice26

Okay ; now i get it ! Thanks (:

11. PaxPolaris

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

12. PaxPolaris

$\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:$\Large \begin{matrix}2m+2w=204 \\ 2m-3w=-6 \\ -\ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}$