Write System of Equations from Context

Question

At a particular restaurant, each slider has 225 calories and each chicken wing has 70 calories. A combination meal with sliders and chicken wings has a total of 10 sliders and chicken wings altogether and contains 1165 calories. Write a system of equations that could be used to determine the number of sliders in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system.

Answer 1

Let s be the number of sliders in the combo meal, and let w be the numbervof wings in the combo meal.

Then s+w = 10, and

225s + 70w = 1,165

A solution was not asked for, only the above equations. But...

Subtracting s from both sides of the first equation:

w = 10 - s

Now substitute this into the second equation:

225s + 70(10-s) = 1165

Simplifying using the distributive law:

225s + 700 - 70s = 1165

Subtracting 700 from both sides and combining the "s" terms:

155s = 465

Dividing both sides by 155:

s = 3

w = 10 - s = 10 - 3 = 7

Checking:

225*3 + 70*7 = 675 + 490 = 1165

By the way, in the context of this particular problem, any solutions involving fractions or negative numbers would indicate either an error in the problem statement or a mistake in the solution process. You can't have a negative slider nor a fraction of a wing!

Answer 2

I went through in detail how to develop the system of equations from the problem statement.