Sharing Mangoes in a Custom Ratio: A Comprehensive Guide

If you have 370 mangoes and you need to distribute them in a specific ratio—1/2, 3/8, and 2/3—this guide will walk you through the process step by step. This method can be applied not only to mangos but also to similar scenarios where you need to distribute items according to given ratios.

Understanding the Problem

When dealing with ratios, like 1/2, 3/8, and 2/3, it might seem challenging to directly apply them to a total of 370 mangoes. However, by finding a common denominator and applying algebra, the process becomes straightforward.

Step 1: Finding a Common Denominator

The first step is to find the lowest common denominator (LCD) of the fractions, which in this case are 1/2, 3/8, and 2/3. LCD (2, 8, 3) 24. This means that 24 is the smallest number that is a multiple of all three denominators.

Step 2: Converting the Fractions

Next, convert each fraction to have a denominator of 24:

1/2 becomes 12/24 3/8 becomes 9/24 2/3 becomes 16/24

The combined ratio in this form is 12:9:16, and the sum of these parts is 37.

Step 3: Solving for the Total Number of Halves

Now, we can set up the equation to find the total number of parts (x) that gives us 370 mangoes:

dfrac{12}{24}x 370

Multiplying both sides by 24:

12x 370 * 24

Solving for x:

x (370 * 24) / 12

x 740 / 1.5 240

Step 4: Calculating Each Share

The next step is to calculate how many mangoes each part of the ratio represents:

1/2 of 240 is 120 mangoes 3/8 of 240 is 90 mangoes 2/3 of 240 is 160 mangoes

Practical Application: Mixology

Suppose you want to blend a special cocktail using these mangoes. Here’s one recipe that incorporates these numbers:

Puree 120 mangoes Add 8/24ths (or 1/3) of vodka (considering 1/24th as 1 tablespoon, so 8 tablespoons of vodka) Add 4/24ths (or 1/6) of lime juice (considering 1/24th as 1 tablespoon, so 4 tablespoons of lime juice) Include 1 tablespoon of maple syrup Top it off with lime wedges

Shake the mixture and serve it in 37 large tumblers. Notice the clever way you can use differently shaped glasses to keep each group’s ratio correct.

Conclusion

By following these steps, you can easily distribute your mangoes in the desired ratio. This method can be applied to any similar distribution problem, making it a versatile and useful technique for both everyday and professional scenarios.