Question

At a particular restaurant, each mini hotdog has 60 calories and each mozzarella stick has 70 calories. A combination meal with mini hotdogs and mozzarella sticks is shown to have 1080 total calories and 5 more mini hotdogs than mozzarella sticks. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of mozzarella sticks in the combination meal. Define the variables that you use to write the system.

Answer 1

There are 9 pizza rolls and 12 mini hotdogs in the combination meal.

Explanation:

We are given the following in the question.

Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.

Total number of items in combination meal = 21

Thus, we can write the equation

Calorie in a pizza roll = 60

Calorie in a mini hotdog = 70

Total calories = 1380

Thus, we can write the equation

Solving the two equations, we get,

Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.

Answer 2

the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.

Explanation:

To determine the number of mini hotdogs and mozzarella sticks in the combination meal, we can use the following system of equations:

Let x be the number of mini hotdogs in the combination meal.

Let y be the number of mozzarella sticks in the combination meal.

The first equation represents the total number of calories in the combination meal: 60x + 70y = 1080

The second equation represents the difference between the number of mini hotdogs and mozzarella sticks: x - y = 5

Thus, the system of equations is:

60x + 70y = 1080

x - y = 5

To solve this system, we can use a variety of methods, such as substitution or elimination. For example, we can eliminate x by adding the equations together, which yields:

60x + 70y = 1080

x - y = 5

60x - x + 70y - y = 1080 - 5

59x + 69y = 1075

Dividing both sides by 59, we find that x = 18.

Substituting this value into the second equation, we find that y = 18 - 5 = 13.

Therefore, the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.