Calculating the Increased Seats Ratio in Mathematics, Physics, and Biology for a School

When a school considers increasing the number of seats for various subjects such as Mathematics, Physics, and Biology, it's important to understand how the proportional increases will affect the overall seat ratio. This article will walk you through the process of calculating the increased seats ratio using different methods and determining the final ratio for each subject.

Method 1: Basic Proportional Increase

Let's start with the initial seat distribution for each subject:

Mathematics: 6x Physics: 7x Biology: 8x

Given the proposal to increase the seats:

Mathematics: 30 seats increase (30% increase) Physics: 50 seats increase (50% increase) Biology: 45 seats increase (45% increase)

Step 1: Calculate the increase for each subject:

Mathematics: 6x * 1.3 7.8x Physics: 7x * 1.5 10.5x Biology: 8x * 1.45 11.6x

Step 2: Form the final ratio:

Ratio of increased seats 7.8x : 10.5x : 11.6x This simplifies to: 78 : 105 : 116

Method 2: Direct Proportional Increase with Simplification

Another way to solve this problem is by directly applying the proportional increase to the original seat ratio:

Mathematics: 6x * 130/100 7.8x Physics: 7x * 150/100 10.5x Biology: 8x * 175/100 11.6x

Therefore, the ratio of increased seats is:

7.8x : 10.5x : 11.6x

Which simplifies to: 78 : 105 : 116

Method 3: Simplified Ratio Application

We can also simplify the ratio in an initial step:

Mathematics: 6x * 1.3 7.8x Physics: 7x * 1.5 10.5x Biology: 8x * 1.45 11.6x

Or in terms of the proportional changes:

Mathematics: 6x * 140/100 7/1 Physics: 7x * 150/100 105x/10 Biology: 8x * 175/100 14/1

Therefore, the ratio is:

7/10 : 105x/10 : 14/10

Which simplifies to: 2 : 3 : 4

Method 4: Percent Proportional Increase

Consider the initial seat ratio and apply the proportional increases:

Mathematics: 6x * 130/100 7.8x Physics: 7x * 150/100 10.5x Biology: 8x * 145/100 11.6x

This also results in the final ratio:

7.8x : 10.5x : 11.6x

Simplified: 78 : 105 : 116

Conclusion

The methods discussed above provide the same results for the final increased seat ratio. For Mathematics, Physics, and Biology, the final ratio of increased seats is 78 : 105 : 116. This understanding is crucial for the school administration to effectively manage resources and allocate spaces according to the increasing needs of each subject.