ALg 2 help plz MATRICES

[hollerback1]

Hey, its me again lol.

I apologize for my actions, now plz help me.

this word problem is based on matrices plz figure this out.

A builder hired carpenters at 16$ per hour, apprentices at 9$ per hour and student helpers at 5$ per hour. Twice as many carpenters as apprentices are hired. If the builder hires 11 people and pays them a total salary of 133$ per hour, how many of each did he hire?

thanks, hollerback1

 

[galactus]

Let a=apprentices
c=carpenters
h=helpers

a+c+h=11. But since there are twice as many carpenters as apprentices, we have c=2a. See?.

The amount of money per hour is 16c+9a+5h=133. Sub in c=2a, this is the portion of the system which helps you eliminate a variable.

a+2a+h=11
16(2a)+9a+5h=133


3a+h=11
41a+5h=133

Solve the system using substitution, elimination, matrices, whatever.

Don't forget to check your answers.

 

[pka]

\(\displaystyle \L
\left[ {\begin{array}
16 & 9 & 5 \\
\end{array}} \right]\left[ {\begin{array}
c \\
a \\
{11 - c - a} \\
\end{array}} \right] = 133\) and \(\displaystyle \L
c = 2a\)

 

[hollerback1]

ty

thank you so much guys from now on i will always ask this site for help. :lol: