Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
peter and arianna just had business cards made. peters printing company charged a one - time setup fee of $4 and then $13 per box of cards. arianna, meanwhile, ordered hers online. they cost $12 per box. there was no setup fee, but she had to pay $20 to have her order shipped to her house. by coincidence, peter and arianna ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend?
peter and arianna each bought \boxed{} boxes of business cards, spending $ \boxed{}.

Explanation:

Step1: Set up equations

Let \(x\) be the number of boxes.
Peter's cost: \(y = 4+13x\)
Arianna's cost: \(y = 20 + 12x\)

Step2: Substitute and solve

Set \(4+13x=20 + 12x\)
\(13x-12x=20 - 4\)
\(x = 16\)

Step3: Find the cost

Substitute \(x = 16\) into Arianna's equation \(y=20+12x\)
\(y=20+12\times16=20 + 192=212\)

Answer:

Peter and Arianna each bought \(16\) boxes of business cards, spending \(\$212\).