Unraveling the Mystery: How Many Mangoes Were in the Bag?
Imagine a scenario where a father sold 60 mangoes, which represent precisely 2/5 of the total mangoes he had in a bag. If you're curious about how many mangoes were originally in the bag, this article will help you calculate it accurately.
Understanding the Problem
The problem provides us with a specific fraction to work with: 2/5 of the total mangoes. This information can be translated into a simple algebraic equation to find the total number of mangoes. Let's denote the total number of mangoes as x.
Setting Up the Equation
The equation based on the given problem is:
[ frac{2}{5} x 60 ]Our goal is to solve for x, the total number of mangoes.
Solving the Equation
To solve for x, we can follow these steps:
1. **Isolate the Variable**: Multiply both sides of the equation by the reciprocal of 2/5, which is 5/2. [ x 60 times frac{5}{2} ] 2. **Perform the Multiplication**: Calculate the right side of the equation. [ x 60 times 2.5 ] 3. **Calculate the Total**: Perform the multiplication to get the value of x. [ x 150 ]Thus, your father originally had 150 mangoes in the bag.
Alternative Methods
However, if you prefer a more intuitive approach, here are some alternative methods to reach the same conclusion:
Using Equivalent Fractions
1. **Identify Equivalent Fractions**: If 60 represents 2/5, then 30 represents 1/5. This is because 60 is 2 times 30. 2. **Find the Total**: Multiply the number representing 1/5 (which is 30) by 5 to get the total number of mangoes. [ 30 times 5 150 ]Using Simple Multiplication
1. **Multiplication Approach**: Since 60 is 2/5 of the total, you can find 1/5 by dividing 60 by 2. Then, multiply 1/5 by 5 to get the total. [ frac{60}{2} 30, 30 times 5 150 ]Verification with Proportions
1. **Setting Up Proportions**: If 60 mangoes is 2/5, then the total (y) can be found by solving the proportion. [ y 60 times frac{5}{2} 150 ]Conclusion
The problem of determining the total number of mangoes in the bag is a straightforward application of fractions and proportions. Whether you use the algebraic method or an intuitive approach, the result is consistently 150 mangoes. This simple calculation can be applied to similar problems involving fractions and proportions.
Real-life Applications
Fractions and proportions are not just mathematical concepts; they have practical applications in everyday life. Understanding how to solve such problems can help in managing resources, budgeting, and even in cooking and baking.
If you have any more questions or need further assistance with solving such problems, feel free to reach out!