Question

At a particular restaurant, each mini hotdog has 70 calories and each chicken wing has 60 calories. A combination meal with mini hotdogs and chicken wings is shown to have 1220 total calories and 10 more mini hotdogs than chicken wings. Determine the number of mini hotdogs in the combination meal and the number of chicken wings in the combination meal.​

Answer 1

• mini hotdogs: 14
• chicken wings: 4

Explanation:

You want the number of mini hotdogs of 70 calories each and chicken wings of 60 calories each in a combination meal with 1220 calories, if there are 10 more mini hotdogs than chicken wings.

Setup

Let c represent the number of chicken wings. Then (c+10) is the number of mini hotdogs, and the calorie count is ...

70(c +10) +60c = 1220

Solution

Simplifying the equation gives ...

130c +700 = 1220

130c = 520 . . . . . . . . subtract 700

c = 4 . . . . . . . . . . . divide by 130

c+10 = 14 . . . . . . the number of mini hotdogs

There are 14 mini hotdogs and 4 chicken wings in the combination meal.

__

Additional comment

The attachment shows the solution of the pair of equations that we could write involving calories and item count.

• 70h +60c = 1220
• h -c = 10

In the above solution we effectively solved these using substitution (substituting c+10 for h).

The equations for most mixture problems can be written using 2 variables, one for each of the quantities you want to find. When one quantity is given in terms of the other, as is usually the case, it can be simpler to use one variable instead of two.

<95141404393>