Solving a Classic Math Puzzle: The Coffee and Donut Riddle

Have you ever encountered a seemingly simple math puzzle that actually takes a bit of algebra to solve? Today, we’ll dive into one of these classic puzzles: the coffee and donut cost riddle. This problem, while seemingly trivial, can be a great way to introduce algebra to beginners. Let's explore how to solve it step by step.

The Riddle: A Coffee and Donut Costs 2.99

The riddle goes like this: 'A coffee and donut cost 2.99. The donut is one dollar more than the coffee. How much does the coffee cost?'

Solving with Algebra

To solve this, we can use algebra. Let:

x the cost of the coffee.

Then, the cost of the donut would be x 1 since the donut is one dollar more than the coffee.

Setting Up the Equation

According to the problem, the total cost of the coffee and donut is 2.99:

x (x 1) 2.99

Simplifying this equation:

2x 1 2.99

Simplifying and Solving

Subtracting 1 from both sides:

2x 1.99

Divide both sides by 2:

x 0.995

Rounded to the nearest cent, the cost of the coffee is $1.00. Therefore:

The donut costs: 0.995 1 1.995 ≈ $2.00

Practical Considerations with Money

In reality, prices are typically rounded to the nearest cent. So, the coffee could be 99 cents and the donut would be $1.99. The combined total would be $2.98, which rounds up to $2.99.

Alternative Interpretation

Some might argue that the problem can be expressed as:

x (x 100) 299

Simplifying:

2x 100 299

Subtracting 100 from both sides:

2x 199

Dividing both sides by 2:

x 99.5

Rounded to the nearest dollar, the cost of the coffee is $99, which seems unrealistic.

Real-World Application

While this problem may seem abstract, it can be applied to more practical scenarios. For example, when working in the 1950s, the rate of pay could be represented similarly to the cost of items. A laborer in Colorado Springs, Colorado, might have made 2.14 dollars per hour in 1959. This suggests that historical pricing might have been quite different from today's standards.

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