Respuesta :
We have a system of equation problem
x= cost of almonds per pound
y= cost of the jelly beans per pound
For the first equation, we have
3 pounds of almonds
8 pounds of jelly beans
total $34
so the equation is
3x+8y=34
For the second equation we have
5 pounds of almonds
2 pounds of jelly beans
total $17
so the equation is
5x+2y=17
so our system of equation is
[tex]\begin{gathered} 3x+8y=34 \\ 5x+2y=17 \end{gathered}[/tex]In order to solve the system we will multiply the second equation by -4
[tex]-4(5x+2y=17)=-20x-8y=-68[/tex]then we sum the equation above with the first equation
[tex]3x-20x+8y-8y=34-68[/tex]then we sum similar terms and isolate the x to find the value of x
[tex]\begin{gathered} -17x=-34 \\ x=\frac{-34}{-17} \\ x=2 \end{gathered}[/tex]then we substitute the value of x=2 in the first equation and we find the value of y
[tex]\begin{gathered} 3(2)+8y=34 \\ 6+8y=34 \\ 8y=34-6 \\ 8y=28 \\ y=\frac{28}{8} \\ y=3.5 \end{gathered}[/tex]The solution is
x= $ 2 cost of each pound of almond
y= $3.50 cost of each pound of jelly beans
