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Sagot :
We can solve this using a system of equations.
Let p be the price of 1 ounce of peanuts and c be the price of 1 ounce of cashews.
"...the first mixture has 15 oz of peanuts combined with 5 oz of cashews, and cost $6." gives us our first equation, that is:
[tex]15p+5c=6[/tex]"...the second mixture has 5 oz of peanuts and 15 oz of cashews, and cost $8." gives us our second equation, that is:
[tex]5p+15c=8[/tex]Thereby, the system would be:
[tex]\begin{cases}15p+5c=6 \\ 5p+15c=8\end{cases}[/tex]Let's mulitply the first equation by -3 and add both of them up:
[tex]\begin{cases}15p+5c=6 \\ 5p+15c=8\end{cases}\rightarrow\begin{cases}-45p-15c=-18 \\ 5p+15c=8\end{cases}\rightarrow-40p=-10[/tex]Solving for p,
[tex]\begin{gathered} -40p=-10\rightarrow p=\frac{-10}{-40}^{} \\ \Rightarrow p=0.25 \end{gathered}[/tex]Let's plug in this value in equation 2 and solve for c, as following:
[tex]\begin{gathered} 5p+15c=8 \\ \rightarrow5(0.25)+15c=8\rightarrow1.25+15c=8\rightarrow15c=6.75\rightarrow c=\frac{6.75}{15} \\ \\ \Rightarrow c=0.45 \end{gathered}[/tex]This way, we would have that
[tex]\begin{gathered} p=0.25 \\ c=0.45 \end{gathered}[/tex]Meaning that an ounce of peanuts costs $0.25, and an ounce of cashews costs $0.45
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