If
3b + 7s + c = 120
4b + 10s + c = 164.5
what is the value of b+s+c ?
My textbook gives 31 as the answer, I cannot understand.
thank you for any help.
Hello, Simone!
There may be an elegant solution . . . but I can't find it.$\displaystyle \begin{array}{cccc}3b + 7s + c & = & 120 & {\color{blue}[1]}\\
4b + 10s + c &= & 164.5& {\color{blue}[2]}\end{array}$
What is the value of $\displaystyle b+s+c$ ?
My textbook gives 31 as the answer.
Subtract [1] from [2]: .$\displaystyle b + 3s \:=\:44.5\quad\Rightarrow\quad s \:=\:\frac{44.5 - b}{3}\;\;{\color{blue}[3]}$
Substitute into [1]: .$\displaystyle 3b + 7\left(\frac{44.4-b}{3}\right) + c\:=\:120\quad\Rightarrow\quad c \:=\:\frac{48.5-2b}{3}\;\;{\color{blue}[4]}$
Consider: .$\displaystyle b + s + c$
Substitute [3] and [4]: .$\displaystyle b + s + c \;=\;b + \frac{44.5-b}{3} + \frac{48.5-2b}{3} \;=\;\frac{3b + 48.5 - b + 44.5 - 2b}{3}$
. . . Therefore: .$\displaystyle b + s + c\;= \;\frac{93}{3}\;=\;31$
Too fast for me, Jhevon!