Solving Math Puzzles: How to Divide 76 Dollars?

Math puzzles can be both challenging and rewarding. One such puzzle involves dividing 76 dollars between two people under specific conditions. Let's explore how to solve such a puzzle using algebraic equations and systematic problem-solving techniques.

The Problem

Two girls have a total of 76 dollars between them. If the first girl gives the second girl seven dollars, they would both have the same amount of money. We need to find out how much money each girl initially had.

Setting Up the Problem

Let x be the amount of money the first girl has.

Let y be the amount of money the second girl has.

We know two things:

x y 76

x - 7 y 7

Let's simplify the second equation:

x - 7 y 7

Subtract 7 from both sides:

x - y 14

Solving the System of Equations

Now we have a system of two equations:

x y 76

x - y 14

Let's add these two equations together:

x y x - y 76 14

Simplifies to:

2x 90

x 45

Now substitute x 45 back into the first equation:

x y 76

45 y 76

y 31

Therefore, the first girl initially had 45 dollars and the second girl had 31 dollars.

Verification

Let's verify the solution:

Check the total amount:

45 31 76

Check if they would have the same amount after the transaction:

45 - 7 38 (first girl)

31 7 38 (second girl)

Both conditions are satisfied.

Conclusion

The first girl had 45 dollars and the second girl had 31 dollars initially. This solution can be found using algebraic equations and systematic problem-solving techniques.

Math Puzzles and Problem-Solving

Math puzzles, like the one above, require critical thinking and algebraic skills. By breaking down the problem and solving it step-by-step, we can arrive at a logical and clear solution. This exercise not only sharpens our problem-solving abilities but also enhances our understanding of mathematical concepts.

Feel free to explore more math puzzles and practice your algebra skills. Happy solving!