Questions: A trucking company had its logo embroidered on the front of baseball caps. It was charged 8.90 per hat plus a one time set up fee of 25. If the project cost 559, how many hats were embroidered?

Transcript text: A trucking company had its logo embroidered on the front of baseball caps. It was charged $\$ 8.90$ per hat plus a one time set up fee of $\$ 25$. If the project cost $\$ 559$, how many hats were embroidered?

Solution

Solution Steps

Step 1: Define the variables

Let $ x $ be the number of hats embroidered.

Step 2: Set up the equation

The total cost is given by the sum of the cost per hat and the one-time setup fee. The cost per hat is $8.90, and the one-time setup fee is $25. The total project cost is $559. Therefore, the equation is: \[ 8.90x + 25 = 559 \]

Step 3: Solve for $ x $

First, subtract the one-time setup fee from the total cost: \[ 8.90x = 559 - 25 \] \[ 8.90x = 534 \]

Next, divide both sides by 8.90 to solve for $ x $: \[ x = \frac{534}{8.90} \] \[ x \approx 60 \]