Solving Balloon Sharing Riddles with Simple Mathematics

Mathematics often presents us with intriguing problems that can challenge our logical reasoning and problem-solving skills. One such problem is the following riddle involving balloons: 'Vivian Alex and Sophie have 140 balloons altogether. Vivian and Alex have the same number of balloons. Alex and Sophie have together 82 balloons. How many balloons does Alex have?'

To break down the problem step by step, let's introduce some variables to make the solution clearer:

Setting Up the Equations

Let's denote:

V as the number of balloons Vivian has. A as the number of balloons Alex has. S as the number of balloons Sophie has.

We can then set up the following equations based on the given information:

V A S 140 (Equation 1) A S 82 (Equation 2)

Solving the Equations

First, let's simplify Equation 1 using the information from Equation 2. If we subtract Equation 2 from Equation 1, we get:

V A S - (A S) 140 - 82

Simplifying this, we get:

V 58

Since V and A are the same (V A), we can now conclude:

Alex has 58 balloons.

Calculation Breakdown

Let's go through the calculations in detail:

We know from Equation 1 that V A S 140. We know from Equation 2 that A S 82. By subtracting Equation 2 from Equation 1, we get V - 82 140 - 82, which simplifies to V 58. Since V A, Alex also has 58 balloons. To find the number of balloons Sophie has, we can use the equation A S 82. So, S 82 - 58 24.

Conclusion

The solution to the riddle is straightforward when we set up and solve the equations properly. Alex has 58 balloons.

Additional Practice

Here are a few more riddles and problems similar to this one that you can try:

If Tom and Jerry have a total of 50 candies, and Tom has 3 times as many candies as Jerry, how many candies does Tom have? If Patrick, Quinn, and Rose have 90 apples altogether, and Patrick and Quinn together have 60 apples, how many apples does Patrick have?

These exercises will help solidify your understanding of algebra and problem-solving skills, making you well-equipped to handle similar riddles and mathematical challenges.