Respuesta :
Let p be the prize of a pen and m the prize of a mechanical pencils. If you buy six pens and one mechanical pencil, you spend 6p+m. We know that this equals 9, because you get 1$ change from a 10$ bill.
Similarly, if you buy four pens and two mechanical pencils, you spend 4p+2m, which is 8$, because now you get a $2 change. Put these equation together in a system:
[tex] \begin{cases} 6p+m=9\\4p+2m=8\end{cases} [/tex]
Now, if you multiply the first equation by 2, the system becomes
[tex] \begin{cases} 12p+2m=18\\4p+2m=8\end{cases} [/tex]
Subtract the second equation from the first:
[tex] 12p+2m - (4p+2m) = 18-8 \iff 8p = 10 \iff p = \dfrac{10}{8} = 1.25 [/tex]
Plug this value into the first equation to get
[tex] 6p+m=9 \iff 6\cdot 1.25 +m = 9 \iff 7.5 +m=9 \iff m = 9-7.5 = 1.5 [/tex]
