Respuesta :
We have to find the price of each pound of almonds and jelly beans.
We can call:
• A: price per pound of the almonds
,• J: price per pound of the jelly beans
We know that 3 pounds of almonds and 8 pounds of jelly beans cost $23.
This means that the cost of the almonds, equal to quantity times price, and the cost of the jelly beans together is equal to $23.
We can write this as:
[tex]3A+8J=23[/tex]We also know that 5 pounds and 2 pounds of jelly beans cost $10. We can write this as:
[tex]5A+2J=10[/tex]We can substract the first equation of 4 times the second equation and it will let us solve for A:
[tex]\begin{gathered} 4(5A+2J)-(3A+8J)=4*10-23 \\ 20A+8J-3A-8J=40-23 \\ (20-3)A+(8-8)J=17 \\ 17A=17 \\ A=\frac{17}{17} \\ A=1 \end{gathered}[/tex]Knowing the price of the almonds (A = 1) we can use any of the original equations to find J:
[tex]\begin{gathered} 5A+2J=10 \\ 5*1+2J=10 \\ 2J=10-5 \\ 2J=5 \\ J=\frac{5}{2} \\ J=2.5 \end{gathered}[/tex]Answer:
Cost for each pound of almonds: $1
Cost for each pound of jelly beans: $2.50
