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 September 6th, 2019, 04:34 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 one-third of the first. The fourth costs as much as the second and third together. How much does each object cost?
 September 7th, 2019, 08:26 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 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, 01:59 PM   #3
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Quote:
 Originally Posted by Yidna What kind of a store where everything's free?
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 one-third 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 02:58 PM.

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