Solving Math Puzzles for Kids: Toni's Money

Math puzzles are a fantastic way to engage young minds and enhance their problem-solving skills. In this article, we will walk through a fun puzzle that involves three friends: Alex, Sonia, and Toni. The challenge is to determine how much money each friend has, given a few clues about their amounts.

Introduction to the Puzzle

The puzzle starts by stating that Alex, Sonia, and Toni have a total of 580 dollars. However, the relationships between the amounts held by each friend are not immediately clear. We can introduce a step-by-step solution to unravel the mystery.

Step-by-Step Solution

First, let's define some variables to represent each person's amount of money:

Alex x Sonia y Toni z

From the given information, we can write the following equations:

x y z 580 (Total amount held by all three friends) y x 120 (Sonia has 120 more than Alex) z y 190 (Toni has 190 more than Sonia)

Now, let's substitute the second and third equations into the first equation to find the value of x, y, and z.

Substitution Process

Starting with the second equation, we can express y in terms of x:

y x 120

Substitute y in the third equation:

z (x 120) 190 x 310

Now, substitute both y and z in the first equation:

x (x 120) (x 310) 580

Combine like terms:

3x 430 580

Isolate x:

3x 580 - 430

3x 150

x 50

Now that we know x, we can find y and z:

y x 120 50 120 170

z y 190 170 190 360

Conclusion

Through step-by-step algebraic manipulation and substitution, we have determined that Toni (Tini) has 360 dollars. This problem serves as a great exercise for young students to practice their problem-solving skills and algebraic reasoning.

In summary, the amount of money each friend has is:

Alex: 50 dollars Sonia: 170 dollars Toni: 360 dollars

This puzzle can be a fun and engaging activity for math classes or homework, helping children develop their logical thinking and numerical skills.

Related Resources

If you are looking to enhance your child's problem-solving skills, consider exploring the following resources:

Math Puzzles for Kids Grade 5 Math Activities Building Problem-Solving Skills

Stay tuned for more engaging and educational content!