In a community service class in the fall, $3$ of the $15$ class sessions were lectures, while all others were devoted to fieldwork in parks. In the spring, the number of sessions devoted to fieldwork remained the same, but the total number of sessions increased to $18$ . In the spring, what percent of class sessions were lectures?

View step-by-step help

Home

Math Problems

Grade 8

Percent of change: word problems

Full solution

Q. In a community service class in the fall,

3

of the

15

class sessions were lectures, while all others were devoted to fieldwork in parks. In the spring, the number of sessions devoted to fieldwork remained the same, but the total number of sessions increased to

18

. In the spring, what percent of class sessions were lectures?

Determine number of lecture sessions: Determine the number of lecture sessions in the fall. $\newline$ Since $3$ of the $15$ class sessions were lectures, we have: $\newline$ Number of lecture sessions in the fall = $3$
Determine number of fieldwork sessions: Determine the number of fieldwork sessions in the fall. $\newline$ Since all other sessions were devoted to fieldwork, we have: $\newline$ Number of fieldwork sessions in the fall $=$ Total sessions $-$ Lecture sessions $\newline$ Number of fieldwork sessions in the fall $= 15 - 3 = 12$
Determine fieldwork sessions in spring: Determine the number of fieldwork sessions in the spring. $\newline$ According to the problem, the number of sessions devoted to fieldwork remained the same in the spring as in the fall. $\newline$ Number of fieldwork sessions in the spring = Number of fieldwork sessions in the fall = $12$
Determine total sessions in spring: Determine the total number of sessions in the spring. $\newline$ The problem states that the total number of sessions increased to $18$ in the spring. $\newline$ Total number of sessions in the spring = $18$
Calculate lecture sessions in spring: Calculate the number of lecture sessions in the spring. $\newline$ Since the number of fieldwork sessions remained the same, the rest of the sessions must be lectures. $\newline$ Number of lecture sessions in the spring $=$ Total sessions in the spring $-$ Fieldwork sessions in the spring $\newline$ Number of lecture sessions in the spring $= 18 - 12 = 6$
Calculate percentage of lecture sessions: Calculate the percentage of lecture sessions in the spring. $\newline$ Percentage of lecture sessions = $(\frac{\text{Number of lecture sessions in the spring}}{\text{Total number of sessions in the spring}}) \times 100\%$ $\newline$ Percentage of lecture sessions = $(\frac{6}{18}) \times 100\%$ $\newline$ Percentage of lecture sessions = $0.333... \times 100\%$ $\newline$ Percentage of lecture sessions = $33.33...\%$