Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Addison and Luke just had business cards made. Addison's printing company charged a one-time setup fee of $4 and then $19 per box of cards. Luke, meanwhile, ordered his online. They cost $18 per box. There was no setup fee, but he had to pay $5 to have his order shipped to his house. By coincidence, Addison and Luke ended up spending the same amount on their business cards. How many boxes did each buy? How much did each spend?

Answer 1

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

`\begin{gathered} T=4+19x \\ \text{where} \\ T=\text{total cost} \\ x=n\\u\text{mber of box} \end{gathered}`

For Luke:

Shipping fee = $5

Cost per box = $18

Similarly, we can get the equation to be

`T=5+18x`

So we have two equations:

`\begin{gathered} T=4+19x---\text{equation 1} \\ T=5+18x---\text{Equation 2} \end{gathered}`

To solve the question, we will substitute the value of T in equation 1 into 2

`4+19x=5+18x`

Simplifying

`\begin{gathered} 19x-18x=5-4 \\ x=1 \end{gathered}`

Thus, they each bought 1 box

To find how much each spent, we will substitute x=1 into the equations

`T=4+19(1)=23`

For the second 1

`T=5+18(1)=23`

Thus, they both spent $23