Math Problem Statement

In your school, the ratio of girls to boys is 3 to 5. There are a total of 168 students in the school. How many boys are there in this school?

Solution

The text in the image asks the following question (translated from Dutch to English):

"In your school, the ratio of girls to boys is 3 to 5. There are a total of 168 students in the school. How many boys are there in this school?"

Solution:

Given:

  • The ratio of girls to boys is 3:53:5.
  • Total number of students = 168.

Let's denote:

  • The number of girls by 3x3x,
  • The number of boys by 5x5x.

According to the problem, the total number of students is the sum of girls and boys:

3x+5x=1683x + 5x = 168

8x=1688x = 168

Now, solve for xx:

x=1688=21x = \frac{168}{8} = 21

Thus, the number of boys is:

5x=5×21=1055x = 5 \times 21 = 105

Answer:

There are 105 boys in the school.

Would you like more details or have any questions about this? Here are five related questions:

  1. If the ratio of girls to boys was 4:5 instead, how many boys would there be in the school?
  2. How many girls are there in the school based on the current ratio?
  3. What is the percentage of boys in the school?
  4. If 20 new girls join the school, what will be the new ratio of girls to boys?
  5. If the total number of students increased to 200 while keeping the same ratio, how many boys would there be?

Tip: When working with ratios, it's helpful to express the total amount as a sum of parts based on the ratio, and then solve for the variable representing one part.

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Math Problem Analysis

Mathematical Concepts

Ratios
Algebra

Formulas

Total Students = Number of Girls + Number of Boys
Number of Students = Ratio × x

Theorems

Proportionality

Suitable Grade Level

Grades 6-8