Q: In a dance class of 20 students, 20% enrolled in contemporary dance, 25% of the remaining enrolled in jazz dance, and the rest enrolled in hip-hop dance. What percentage of the entire students enrolled in hip-hop dance? A: Let’s first understand the problem, extract relevant variables and their corresponding numerals, and make a complete plan. Then, let’s carry out the plan, calculate intermediate variables (pay attention to correct numerical calculation and commonsense), solve the problem step by step, and show the answer.
Plan:
- Calculate the number of students who enrolled in contemporary dance.
- Subtract this from the total number of students to find the number of students who did not enroll in contemporary dance.
- Calculate the number of these students who then enrolled in jazz dance.
- Subtract the number of students who enrolled in jazz dance from the total number of students who did not enroll in contemporary dance to find the number of students who enrolled in hip-hop dance.
- Calculate the percentage of the entire student body that enrolled in hip-hop dance.
Let's start with Step 1:
Step 1:
Calculate the number of students who enrolled in contemporary dance.
Total Students = 20
Percentage Enrolling in Contemporary Dance = 20%
Number of Students Enrolling in Contemporary Dance = Total Students x Percentage Enrolling in Contemporary Dance
= 20 x 0.20
= 4
So, there are 4 students who enrolled in contemporary dance.
Now we move on to Step 2:
Step 2:
Subtract this from the total number of students to find the number of students who did not enroll in contemporary dance.
Students Not Enrolling in Contemporary Dance = Total Students - Number of Students Enrolling in Contemporary Dance
= 20 - 4
= 16
Next, we move on to Step 3:
Step 3:
Calculate the number of these students who then enrolled in jazz dance.
Percentage Enrolling in Jazz Dance = 25%
Number of Students Enrolling in Jazz Dance = Students Not Enrolling in Contemporary Dance x Percentage Enrolling in Jazz Dance
= 16 x 0.25
= 4
Finally, we move on to Step 4:
Step 4:
Subtract the number of students who enrolled in jazz dance from the total number of students who did not enroll in contemporary dance to find the number of students who enrolled in hip-hop dance.
Students Enrolling in Hip Hop Dance = Students Not Enrolling in Contemporary Dance - Number of Students Enrolling in Jazz Dance
= 16 - 4
= 12
Now we can calculate the percentage of the entire student body that enrolled in hip-hop dance using the formula:
Percentage Enrolling in Hip Hop Dance = (Students Enrolling in Hip Hop Dance / Total Students) x 100%
Plugging in our values:
Percentage Enrolling in Hip Hop Dance = (12 / 20) x 100%
= 0.6 x 100%
= 60%
Therefore, 60% of the entire student body enrolled in hip-hop dance.
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