Examkin

Question

Difficulty: MediumPercents and Percent Change

In a certain school district, the number of students enrolled in high school chemistry was 20%20\% of the total number of high school students. After a new curriculum was introduced, the number of chemistry students increased by 35%35\%, while the total number of high school students in the district remained the same. What percent of the total high school student population was enrolled in chemistry after the curriculum change?

  1. A
    7%7\%
  2. 27%27\%Answer
  3. C
    48%48\%
  4. D
    55%55\%

Answer

27%27\%
To find the new percentage of students enrolled in chemistry, we can express the initial enrollment in terms of the total student population, TT. Initially, the number of chemistry students is 0.20T0.20T. An increase of 35%35\% on this enrollment is calculated by multiplying the initial enrollment by 1.351.35. This gives the new enrollment as 0.20T×1.35=0.27T0.20T \times 1.35 = 0.27T. Since the total number of students TT remains unchanged, the new enrollment represents 27%27\% of the total population.

Step-by-Step Solution

1
Define variables for the initial values.
Let the total number of high school students in the district be TT. The initial number of chemistry students is 0.20T0.20T.
Establishing algebraic representations helps organize the relation between the variables.
2
Calculate the new number of chemistry students after the 35%35\% increase.
The new number of chemistry students is 0.20T×(1+0.35)=0.20T×1.35=0.27T0.20T \times (1 + 0.35) = 0.20T \times 1.35 = 0.27T.
An increase of 35%35\% means multiplying the initial value by 1.351.35.
3
Calculate the new percentage of the total student population.
Since the total student population TT remained the same, the new fraction of chemistry students is 0.27TT=0.27\frac{0.27T}{T} = 0.27, which is 27%27\%.
Dividing the new number of chemistry students by the total student population gives the final percentage.

Key Concept

Calculating percentage changes on a subgroup relative to a constant total population.
Rate this question

Topics

Percents and Percent Change

More questions from this topic