Question

At a particular restaurant, each mini hotdog has 70 calories and each pizza roll has 50 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 1190 total calories and twice as many pizza rolls as there are mini hotdogs. Determine the number of mini hotdogs in the combination meal and the number of pizza rolls in the combination meal.

Answer 1

The combination meal at the restaurant includes 7 mini hotdogs and 14 pizza rolls, determined by setting up and solving a system of equations based on the calorie content of each item and the total calories.

Step-by-step explanation:

We need to determine the number of mini hotdogs and pizza rolls in a combination meal based on their caloric information. Each mini hotdog has 70 calories, and each pizza roll has 50 calories. The entire meal has 1190 calories, and there are twice as many pizza rolls as mini hotdogs.

Step-by-step solution:

1. Let's denote the number of mini hotdogs as x and the number of pizza rolls as 2x, since there are twice as many pizza rolls.
2. The total calories from mini hotdogs are 70x, and from pizza rolls are 50(2x) or 100x.
3. Combining both, we get the total calorie equation: 70x + 100x = 1190.
4. Simplify the equation: 170x = 1190.
5. Solve for x: x = 1190 / 170.
6. Calculate x: x = 7. Therefore, there are 7 mini hotdogs.
7. Since there are twice as many pizza rolls, calculate 2x: 2x = 2 * 7.
8. There are 14 pizza rolls.

So, the combination meal includes 7 mini hotdogs and 14 pizza rolls.