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September 6th, 2019, 05:34 PM  #1 
Newbie Joined: Jun 2019 From: New York Posts: 2 Thanks: 0  Help with a problem please
There are 4 objects in a store. The first object costs as much as the second plus half of the third. The second costs as much as the fourth minus the third . The third costs onethird of the first. The fourth costs as much as the second and third together. How much does each object cost?

September 7th, 2019, 09:26 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,636 Thanks: 1472 
This is all pretty straightforward if tedious. Using matrix notation $\begin{pmatrix}p_1\\p_2\\p_3\\p_4\end{pmatrix} = \begin{pmatrix} 0 &1 &\dfrac 1 2 &0\\ 0 &0 &1 &1\\ \dfrac 1 3 &0 &0 &0\\ 0 &1 &1 &0 \end{pmatrix}\begin{pmatrix}p_1\\p_2\\p_3\\p_4\end {pmatrix}$ $\begin{pmatrix}0\\0\\0\\0\end{pmatrix} = \begin{pmatrix} 1 &1 &\dfrac 1 2 &0\\ 0 &1 &1 &1\\ \dfrac 1 3 &0 &1 &0\\ 0 &1 &1 &1 \end{pmatrix}\begin{pmatrix}p_1\\p_2\\p_3\\p_4\end {pmatrix}$ There is no definite solution to this equation. $\begin{pmatrix}p_1\\p_2\\p_3\\p_4\end{pmatrix} = c \begin{pmatrix}6\\5\\2\\7\end{pmatrix}, \forall c\geq 0$ 
September 12th, 2019, 02:59 PM  #3 
Newbie Joined: Sep 2019 From: British Columbia, Canada Posts: 19 Thanks: 1  There are 4 objects in a store. The first object costs as much as the second plus half of the third. The second costs as much as the fourth minus the third . The third costs onethird of the first. The fourth costs as much as the second and third together. How much does each object cost? a = 3x b = 2.5x c = $x d = 3.5x Last edited by Yidna; September 12th, 2019 at 03:58 PM. 