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 and a desk for $77. Find the price of a chair, a table, and a desk.

C hai r = x
T ab l e = y
Des k = 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}}}}

Answered by D3xt3R | 2024-06-10

The chair costs $17, the table costs $23, and the desk costs $60. This is determined by solving a system of equations based on the prices given for various combinations of the items. Using algebra, we isolate variables to find the individual prices.
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Answered by D3xt3R | 2024-12-20