Solving Math Word Problems: The Rock Problem

Math word problems can often be challenging, requiring careful reading and logical reasoning. This article explores a specific problem involving rocks and two individuals: Chris and Gordon. Let's break down the problem step-by-step to find the solution.

Solving the Rock Problem

The problem states that Chris has 4 more than twice as many rocks in his wagon as Gordon has in his. If Chris gives Gordon 6 rocks, he will have 1 more rock than Gordon. We need to determine how many rocks each person originally had.

First, let's define the variables:

nC represents the number of rocks Chris originally has. nG represents the number of rocks Gordon originally has.

The problem gives us two key pieces of information:

First Clue: Chris's Number of Rocks

The first clue states that Chris has 4 more than twice as many rocks as Gordon. This can be written as:

nC 2nG 4

Second Clue: After Giving Rocks

The second clue states that if Chris gives Gordon 6 rocks, he will have 1 more rock than Gordon. This can be expressed as:

(nC - 6) nG 6 1

Which simplifies to:

nC - 6 nG 7

And thus:

nC nG 13

Eliminating the Variable

Now we have two equations:

nC 2nG 4 nC nG 13

By setting these equations equal to each other, we can solve for nG:

2nG 4 nG 13

Solving for nG, we subtract nG from both sides:

nG 4 13

Subtract 4 from both sides:

nG 9

Finding nC

Now that we know nG, we can find nC using one of our original equations:

nC 2nG 4

Substitute nG 9 into the equation:

nC 2(9) 4

nC 18 4

nC 22

So, Chris originally had 22 rocks and Gordon originally had 9 rocks.

After the Exchange

After Chris gives Gordon 6 rocks, his number of rocks becomes:

22 - 6 16

And Gordon's number of rocks becomes:

9 6 15

Confirming that Chris now has 1 more rock than Gordon:

16 15 1

Conclusion

This problem exemplifies how mathematical reasoning and algebra can be used to solve word problems. By defining variables, setting up equations, and solving them step-by-step, we can determine the original number of rocks each person had and verify the outcomes after the exchange.

Math word problems are a valuable tool for enhancing mathematical skills and logical thinking. Understanding how to break down and solve such problems can be applied to various real-life situations, not just in math classes.