Calculate the Count of Seventh and Eighth Graders Using Percentages

Question

A group of students and teachers go on a school trip, of which 180 are students.
25% of the group are from the eighth grade, 20% are from the ninth grade, 40% are from the seventh grade, and the rest of the group are teachers.

How many students from the seventh and eighth grades go on the trip?

Video Solution

Solution Steps

00:00 Determine how many students participated from grades 7 and 8
00:05 The formula for converting percentages to fractions
00:18 Calculate the percentage of students from grade 8
00:26 Apply the formula to convert from percentages to fractions
00:33 Multiply the fraction by the total number of students to be found
00:38 Factor and simplify wherever possible
00:48 This is the number of students from grade 8
00:56 Apply the same method to determine the number of students in grade 7
01:07 Convert percentages to fractions and multiply by the number of students
01:17 Factor and simplify wherever possible
01:34 This is the number of students from grade 7
01:43 Proceed to add together the total number of students in grades 7+8
01:48 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the number of eighth-grade students
  • Step 2: Calculate the number of seventh-grade students
  • Step 3: Sum the number of students from the seventh and eighth grades

Now, let's work through each step:
Step 1: The eighth-grade students make up 25% of the students. Therefore, the number of eighth-grade students is 180×25100=45 180 \times \frac{25}{100} = 45 students.

Step 2: The seventh-grade students make up 40% of the students. Therefore, the number of seventh-grade students is 180×40100=72 180 \times \frac{40}{100} = 72 students.

Step 3: Adding the number of students from the seventh and eighth grades gives us: 45+72=117 45 + 72 = 117 students.

Therefore, the number of students from the seventh and eighth grades that go on the trip is 117 students.

Answer

117 students