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PilotLPTM [1.2K]
3 years ago
9

A dealer sells a certain type of chair and a table for $40. He also sells the same sort of table and a desk for $83 or a chair a

nd a desk for $77. Find the price of a chair, table, and of a desk.
Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0
Chair=x

Table=y

Desk=z

\begin{Bmatrix}x+y&=&40\\y+z&=&83\\x+z&=&77\end{matrix}

keep the first row as normal, then in the other ones, we can isolate Y and X

\begin{Bmatrix}x+y&=&40\\y&=&83-z\\x&=&77-z\end{matrix}

now we can replace at first row...

\begin{Bmatrix}(77-z)+(83-z)&=&40\\y&=&83-z\\x&=&77-z\end{matrix}

\begin{Bmatrix}160-2z&=&40\\y&=&83-z\\x&=&77-z\end{matrix}

\begin{Bmatrix}-2z&=&40-160\\y&=&83-z\\x&=&77-z\end{matrix}

\begin{Bmatrix}-2z&=&-120\\y&=&83-z\\x&=&77-z\end{matrix}

\begin{Bmatrix}z&=&60\\y&=&83-z\\x&=&77-z\end{matrix}

now we can replace the Z to discovery the other value

\begin{Bmatrix}z&=&60\\y&=&83-60\\x&=&77-60\end{matrix}

\boxed{\boxed{\boxed{\begin{Bmatrix}Chair&=&17\\Table&=&23\\Desk&=&60\end{matrix}}}}
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