At a particular restaurant, each mini hotdog has 90 calories and each pizza roll has 50 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 860 total calories and 6 more pizza rolls than mini hotdogs. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of pizza rolls in the combination meal. Define the variables that you use to write

To solve the problem, we need to define our variables and set up a system of equations based on the information provided. ### Step 1: Define the Variables Let: - \( h \) = number of mini hotdogs - \( r \) = number of pizza rolls ### Step 2: Set Up the Equations From the problem, we have two key pieces of information: 1. The total calorie count of the combination meal is 860 calories. - Each mini hotdog has 90 calories, so the total calories from mini hotdogs is \( 90h \). - Each pizza roll has 50 calories, so the total calories from pizza rolls is \( 50r \). - Therefore, the first equation based on total calories is: \[ 90h + 50r = 860 \] 2. There are 6 more pizza rolls than mini hotdogs. - This gives us the second equation: \[ r = h + 6 \] ### Step 3: Write the System of Equations The system of equations that can be used to determine the number of mini hotdogs and pizza rolls is: \[ \begin{align*} 1. & \quad 90h + 50r = 860 \\ 2. & \quad r = h + 6 \end{align*} \] This system can now be solved to find the values of \( h \) and \( r \).