Calculate the Count of Seventh and Eighth Graders Using Percentages

Q: How do I convert percentages to decimals for calculations?

Divide the percentage by 100: $ 25\% = \frac{25}{100} = 0.25 $. Then multiply: $ 180 \times 0.25 = 45 $.

Q: What if the percentages don't add up to 100%?

In this problem, teachers make up the remaining percentage. If students are 85% total (25% + 20% + 40%), then teachers are 15% of the group.

Q: Can I solve this problem a different way?

Yes! You could also use fractions: $ \frac{25}{100} \times 180 = \frac{25 \times 180}{100} = \frac{4500}{100} = 45 $ students.

Q: How do I check if my final answer makes sense?

Add your answers: 45 + 72 = 117 students. This should be less than the total of 180 students, which it is. Also verify: $ \frac{117}{180} = 0.65 = 65\% $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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?

2

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 $180 \times \frac{25}{100} = 45$ students.

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

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

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

3

Final Answer

117 students

Key Points to Remember

Essential concepts to master this topic

Percentage Rule: Multiply total by percentage as decimal to find part
Technique: Calculate 25% of 180 = 180 × 0.25 = 45 students
Check: Sum all percentages: 25% + 20% + 40% + 15% = 100% ✓

Common Mistakes

Avoid these frequent errors

Adding percentages instead of calculating individual amounts
Don't add 25% + 40% = 65% and call it 65 students! This ignores the total group size of 180. Always multiply each percentage by the total: (25% × 180) + (40% × 180) = 45 + 72 = 117 students.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why can't I just add the percentages 25% + 40% = 65%?

+

Percentages alone don't tell you actual numbers! You need to multiply each percentage by the total to find how many students. 25% of 180 = 45 students, and 40% of 180 = 72 students.

How do I convert percentages to decimals for calculations?

+

Divide the percentage by 100: $25\% = \frac{25}{100} = 0.25$ . Then multiply: $180 \times 0.25 = 45$ .

What if the percentages don't add up to 100%?

+

In this problem, teachers make up the remaining percentage. If students are 85% total (25% + 20% + 40%), then teachers are 15% of the group.

Can I solve this problem a different way?

+

Yes! You could also use fractions: $\frac{25}{100} \times 180 = \frac{25 \times 180}{100} = \frac{4500}{100} = 45$ students.

How do I check if my final answer makes sense?

+

Add your answers: 45 + 72 = 117 students. This should be less than the total of 180 students, which it is. Also verify: $\frac{117}{180} = 0.65 = 65\%$ ✓

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