Respuesta :
hello
to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.
let x represent the cost of avocados
let y represent the cost of tomatoes
[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]from equation 1, let's make xthe subject of formula
[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]put equation 3 into equation 2
[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]since y = 2.35, let's put that in either equation 1 or 2
from equation 2
3x + 8y = 22.55
put y = 2.35 and solve for x
[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively
