Have you ever found yourself in a mathematical conundrum, trying to figure out the cost of a single taco? Well, fear not! We’re here to solve the taco mystery and put your mathematical skills to the test.
Let’s break down the problem at hand. According to the given information, we know that 2 tacos and 6 drinks cost $22, and 3 tacos and 6 drinks cost $27. Our mission is to determine the cost of a single taco.
Step 1: Establish a Baseline
To begin, let’s assign variables to the unknowns. Let “x” represent the cost of a taco and “y” represent the cost of a drink. With this in mind, we can create two equations based on the given information:
Equation 1: 2x + 6y = 22
Equation 2: 3x + 6y = 27
Step 2: Simplify the Equations
Now, let’s simplify the equations to make them easier to work with. We can start by subtracting Equation 1 from Equation 2:
(3x + 6y) – (2x + 6y) = 27 – 22
x = 5
Step 3: Find the Cost of a Taco
Great! We’ve determined that the cost of a taco is $5. But let’s not stop there. We can double-check our answer by substituting the value of x back into one of the original equations.
Using Equation 1:
2(5) + 6y = 22
10 + 6y = 22
6y = 12
y = 2
Step 4: Verify the Solution
With the cost of a taco at $5 and the cost of a drink at $2, let’s ensure that our solution satisfies both equations:
Equation 1: 2(5) + 6(2) = 22
10 + 12 = 22
22 = 22 (True!)
Equation 2: 3(5) + 6(2) = 27
15 + 12 = 27
27 = 27 (True!)
Conclusion
After careful calculations and verification, we can confidently say that a taco costs $5. The mystery has been solved! So, the next time you find yourself pondering the cost of a taco, remember this mathematical adventure and put your problem-solving skills to the test.
Now, go forth and enjoy your delicious tacos, knowing exactly how much they cost!