Solving Ratio Problems: Determining the Weight of the Heavier Girl
Solving Ratio Problems: Determining the Weight of the Heavier Girl
Understanding and applying ratios in real-world scenarios can be a useful skill in a variety of contexts, ranging from basic math problems to more complex scientific and engineering applications. In this article, we will walk through the process of solving a ratio problem involving the weights of two girls.
The problem we are addressing is: The ratio of the weight of two girls is 4:5. If the lighter one weighs 44 kg, what does the heavier one weigh?
Understanding the Ratio
To begin, let's break down the given information. The ratio of the weights of the two girls is 4:5. This means that for every 4 units of weight, the lighter girl has, the heavier girl has 5 units of weight.
Setting Up the Equation
We can represent the weight of the lighter girl as 4x and the weight of the heavier girl as 5x, where x is a common multiplier. According to the problem, the weight of the lighter girl is 44 kg. Therefore, we can set up the following equation:
4x 44
Solving for x
To find the value of x, we need to isolate it on one side of the equation. We do this by dividing both sides of the equation by 4:
x 44 ÷ 4 11
Calculating the Weight of the Heavier Girl
Now that we know the value of x, we can determine the weight of the heavier girl by multiplying 5 by x:
5x 5 × 11 55 kg
Therefore, the weight of the heavier girl is 55 kg.
Verifying the Solution
To ensure our solution is correct, let's verify it by checking the ratio. If the lighter girl weighs 44 kg, and the heavier girl weighs 55 kg, the ratio of their weights can be expressed as:
44:55 4:5
This confirms that our solution is correct.
Practical Applications
Ratio problems like this one are not just theoretical exercises but have practical applications in many fields. In healthcare, for example, understanding ratios can help in determining the correct dosages of medication. In sports and fitness, they can be used to understand proportional growth and weight.
Conclusion
Solving ratio problems involves setting up and solving equations. By understanding the given ratio and using algebraic methods, we can determine unknown quantities. In this case, we found that if the lighter girl weighs 44 kg, the heavier girl weighs 55 kg, given the ratio of their weights is 4:5.