## bprice26 Group Title 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

1. PaxPolaris Group Title

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 Group Title

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

3. PaxPolaris Group Title

multiply the first eq by 2

4. PaxPolaris Group Title

then subtract the second equation

5. bprice26 Group Title

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 Group Title

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

7. bprice26 Group Title

Okay well how does the substituion method work ?

8. PaxPolaris Group Title

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

9. PaxPolaris Group Title

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

10. bprice26 Group Title

Okay ; now i get it ! Thanks (:

11. PaxPolaris Group Title

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

12. PaxPolaris Group Title

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