The Cost of Soda and Bottle: A Simple Algebraic Solution

Suppose you come across a riddle about the cost of a soda and its bottle. The riddle states that a bottle of soda costs 4.50, and the bottle itself costs 3 more than the soda. This article explores how to solve this riddle using basic algebraic equations. Let's break it down step by step.

Solving the Riddle Using Algebra

First, let’s denote the cost of the soda as x. According to the problem, the bottle costs 3 more than the soda, which can be expressed as x 3.

Given that the total cost of the soda and the bottle is 4.50, we can write the equation as:

x (x 3) 4.50

Combining like terms on the left side of the equation, we get:

2x 3 4.50

Subtracting 3 from both sides to isolate the term with x, we have:

2x 1.50

Now, we divide both sides by 2 to solve for x:

x 0.75

Therefore, the cost of the soda is 0.75, or 75 cents.

Verification of the Solution

To verify our solution, let's take a closer look at the calculations:

The first problem: We denote the cost of the soda as x, and the cost of the bottle as x 3. The total cost is 4.50. The equation is: x (x 3) 4.50 2x 3 4.50 2x 1.50 x 0.75 Since x 0.75, the bottle costs 3 more: 0.75 3 3.75.

This confirms that the cost of the soda is 0.75 and the cost of the bottle is 3.75, which sums up to 4.50.

Conclusion

In conclusion, we have demonstrated a clear and logical approach to solving the riddle about the cost of soda and a bottle. By using basic algebraic equations, we determined that the soda costs 0.75 cents, given the total cost of 4.50 and the relationship between the soda and the bottle's price.

If you are tackling similar algebraic problems or need to enhance your problem-solving skills in mathematics, this riddle serves as a good exercise to practice your algebraic techniques.