A college writing seminar increased its size by $50 \%$ from the first to the second day. If the total number of students in the seminar on the second day was $15$ , how many students were in the class on the first day? $\newline$ Choose $1$ answer: $\newline$ (A) $8$ $\newline$ (B) $\mathbf{1 0}$ $\newline$ (C) $23$ $\newline$ (D) $30$

Full solution

Q. A college writing seminar increased its size by

50 \%

from the first to the second day. If the total number of students in the seminar on the second day was

15

, how many students were in the class on the first day?

\newline

Choose

1

answer:

\newline

(A)

8

\newline

(B)

\mathbf{1 0}

\newline

(C)

23

\newline

(D)

30

Denoting the number of students: Let's denote the number of students on the first day as $x$ . According to the problem, the class size increased by $50\%$ from the first day to the second day. This means that the number of students on the second day is $1.5$ times the number of students on the first day. $\newline$ Mathematically, this can be expressed as: $\newline$ Number of students on the second day = $x + (50\% \text{ of } x) = x + 0.5x = 1.5x$ $\newline$ We are given that the number of students on the second day is $15$ . $\newline$ So, we can set up the equation: $\newline$ $1.5x = 15$
Expressing the number of students on the second day: Now, we need to solve for $x$ to find out how many students were there on the first day. $\newline$ Divide both sides of the equation by $1.5$ to isolate $x$ : $\newline$ $x = \frac{15}{1.5}$
Setting up the equation: Perform the division to find the value of $x$ : $x = \frac{\text{10}}{\text{2}}$ This means there were $10$ students in the class on the first day.