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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

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

    • 2 years ago
  2. bprice26 Group Title
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    i already had an equation written out ; i just don't know what to do from there ..

    • 2 years ago
  3. PaxPolaris Group Title
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    multiply the first eq by 2

    • 2 years ago
  4. PaxPolaris Group Title
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    then subtract the second equation

    • 2 years ago
  5. bprice26 Group Title
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    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
  6. PaxPolaris Group Title
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    Well actually there are to methods, the use of simultaneous equations that i used above and using substitution...

    • 2 years ago
  7. bprice26 Group Title
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    Okay well how does the substituion method work ?

    • 2 years ago
  8. PaxPolaris Group Title
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    *2 methods Using substitution: \[\large m+w= 102\]\[\large \implies w=102-m\] put that in 2nd equation

    • 2 years ago
  9. PaxPolaris Group Title
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    \[\large 2m-3\left( 102-m \right)=-6\]

    • 2 years ago
  10. bprice26 Group Title
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    Okay ; now i get it ! Thanks (:

    • 2 years ago
  11. PaxPolaris Group Title
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    \[\large \implies 2m-306+3m=-6\]\[\large \implies 5m=306-6\]\[\large \implies 5m=300\]

    • 2 years ago
  12. PaxPolaris Group Title
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    \[\Large m=60\]\[\Large w={\large 102-60}=42\] Using simultaneous equations:\[\large m+w=102\]\[\large \implies 2m+2w=204\] Subtracting the second equation:\[\Large \begin{matrix}2m+2w=204 \\ 2m-3w=-6 \\ -\ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}\]

    • 2 years ago
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