Solving the Bacon and Egg Dilemma: How Much Does a Family Pay for 16 Eggs and 10 Strips of Bacon?
When it comes to breakfast, the classic combination of bacon and eggs is a staple in many households. But have you ever wondered how much you’re actually spending on this hearty meal? Let’s take a closer look at the cost of this breakfast favorite, using a simple mathematical problem as our guide: “3 eggs and 4 strips of bacon cost .10. 5 eggs and 1 strip of bacon cost .90. If a family orders 16 eggs and 10 strips of bacon, how much, in dollars, do they pay?”
Understanding the Problem
The problem at hand is a classic example of a system of linear equations. In this case, we have two equations with two variables (the cost of eggs and bacon). The goal is to find the values of these variables that satisfy both equations simultaneously.
Setting Up the Equations
Let’s denote the cost of an egg as E and the cost of a strip of bacon as B. From the problem, we can set up the following equations:
- 3E + 4B = .10
- 5E + B = .90
Solving the Equations
To solve these equations, we can use a method called substitution or elimination. For simplicity, let’s use the elimination method. We can multiply the second equation by 4 and subtract the first equation from the result:
- 20E + 4B = .60
- 3E + 4B = .10
- —————–
- 17E = .50
Dividing both sides of the equation by 17, we find that E (the cost of an egg) is approximately {{ $content }}.97. Substituting E = {{ $content }}.97 into the first equation, we can solve for B (the cost of a strip of bacon), which comes out to be approximately {{ $content }}.28.
Calculating the Total Cost
Now that we know the cost of an egg and a strip of bacon, we can calculate the total cost for 16 eggs and 10 strips of bacon:
- 16E + 10B = 16({{ $content }}.97) + 10({{ $content }}.28) = .52 + .80 = .32
So, a family ordering 16 eggs and 10 strips of bacon would pay approximately .32.
Conclusion
Understanding the cost of your breakfast can be a fun exercise in practical math. By breaking down the problem into manageable steps, we can solve for the cost of individual items and calculate the total cost of a meal. So next time you’re enjoying your bacon and eggs, you’ll know exactly how much you’re paying for that deliciousness.