Solving Word Problems: Determining the Jar’s Capacity

Word problems in mathematics can be challenging, but they offer practical applications to everyday scenarios. One such problem involves a jar with a specific part filled and the addition of water to reach full capacity. Let's explore how to solve such problems step-by-step using the example of a jar that is 2/5 filled with water, and adding 750ml makes it full.

The Problem and the Given Information

A jar is 2/5 filled with water. When 750ml of water is added, it becomes full. The task is to determine the capacity of the jar.

Step-by-Step Solution

Step 1: Understanding the Given Information

The jar is initially 2/5 filled, and 750ml is added to make it full. This implies that the remaining 3/5 of the jar is equivalent to the 750ml added.

Step 2: Finding One Fifth of the Jar

We need to find the volume of 1/5 of the jar. Since 3/5 of the jar equals 750ml, we can set up the equation:

3/5 of the jar 750ml

To find 1/5 of the jar, we divide 750ml by 3:

1/5 of the jar 750ml ÷ 3 250ml

Step 3: Calculating the Full Capacity

Now that we know 1/5 of the jar is 250ml, we can find the total capacity by multiplying 250ml by 5 (since 5/5 1 full jar):

Capacity of the jar 250ml × 5 1250ml

Alternative Solution

We can also solve the problem using algebra. Let's denote the capacity of the jar as x. When the jar is 2/5 filled, the amount of water in it is 2/5 x. When 750ml is added, it becomes full. Therefore, we can set up the equation:

2x/5 750 x

Isolating x on one side:

750 x - 2x/5

Multiplying through by 5 to clear the fraction:

3750 5x - 2x

3750 3x

Dividing both sides by 3:

x 1250ml

Conclusion

Thus, the capacity of the jar is 1250ml, or 1 and a quarter liters. By understanding the problem and breaking it down into manageable steps, we can solve it accurately and efficiently.

Additional Tips for Solving Word Problems

1. Identify the given information and what is being asked. Clearly define the variables and the goal of the problem. 2. Set up equations based on the problem's description. Use fractions, algebra, or any relevant mathematical tools to represent the relationships in the problem. 3. Check your solution. Ensure that your answer satisfies the conditions of the problem and makes practical sense.