To solve the question, we need to set up a system of equation
For Addison:
A one-time setup fee of $4 means a fixed cost
$19 per box is an additional charge that increases as the number of bor increases
we can get the equation as follow
[tex]\begin{gathered} T=4+19x \\ \text{where} \\ T=\text{total cost} \\ x=n\nu\text{mber of box} \end{gathered}[/tex]For Luke:
Shipping fee = $5
Cost per box = $18
Similarly, we can get the equation to be
[tex]T=5+18x[/tex]So we have two equations:
[tex]\begin{gathered} T=4+19x---\text{equation 1} \\ T=5+18x---\text{Equation 2} \end{gathered}[/tex]To solve the question, we will substitute the value of T in equation 1 into 2
[tex]4+19x=5+18x[/tex]Simplifying
[tex]\begin{gathered} 19x-18x=5-4 \\ x=1 \end{gathered}[/tex]Thus, they each bought 1 box
To find how much each spent, we will substitute x=1 into the equations
[tex]T=4+19(1)=23[/tex]For the second 1
[tex]T=5+18(1)=23[/tex]Thus, they both spent $23
