Determining the Ratio of Increased Seats in Mathematics, Physics, and Biology
When dealing with seat allocation in a school, understanding the ratio and the effect of seat increases is a crucial task for administrators and educators. This article will guide you through a step-by-step process to determine the new ratio of seats after a proposal to increase existing seats in mathematics, physics, and biology. We will use the given initial ratio and the proposed increases to find the final ratio.
Understanding the Initial Ratio
The initial number of seats in a school is given in the ratio of 5 : 7 : 8 for mathematics, physics, and biology, respectively. Let's represent these seats in terms of a variable, x. Thus, the initial number of seats can be defined as:
Mathematics: 5x Physics: 7x Biology: 8xCalculating the Increased Number of Seats
The proposal is to increase these seats by 40% for mathematics, 50% for physics, and 25% for biology. We will now calculate the new number of seats after these increases.
Mathematics
For mathematics, the increase is 40%, which can be written as 0.40 or 40/100. Therefore:
New Mathematics seats 5x 0.40 × 5x 5x × 1.40 7x
Physics
For physics, the increase is 50%, which can be written as 0.50 or 50/100. Thus:
New Physics seats 7x 0.50 × 7x 7x × 1.50 10.5x
Biology
For biology, the increase is 25%, which can be written as 0.25 or 25/100. Hence:
New Biology seats 8x 0.25 × 8x 8x × 1.25 1
Now we have the new number of seats:
Mathematics: 7x Physics: 10.5x Biology: 1Expressing the Ratio in Terms of x
To express these in terms of x, we get:
New ratio 7x : 10.5x : 1
We then simplify this ratio by dividing each term by x:
7 : 10.5 : 10
To eliminate the decimal in the ratio, we multiply each term by 2:
14 : 21 : 20
Since there are no common factors among 14, 21, and 20, the ratio is already in its simplest form.
Final Ratio of Increased Seats for Mathematics, Physics, and Biology
Therefore, the final ratio of the increased seats for mathematics, physics, and biology is:
14 : 21 : 20
This systematic approach helps in clearly understanding how seat allocations can be adjusted based on specific percentage increases. By applying these principles, administrators can make informed decisions to optimize resources and meet the needs of students across different subjects.