The ratio of the number of girls to the number of boys in a swimming club was 7 : 2 at first. When 63 new members joined the club, the total number of members in the swimming club became 1 440. How many girls were in the swimming club at first?



Let the number of girls in the swimming club at first be \( 7x \) and the number of boys be \( 2x \), based on the given ratio of girls to boys, \( 7:2 \).

Thus, the total number of members in the club at first is:

\[
7x + 2x = 9x
\]

We are also told that 63 new members joined the club, bringing the total number of members to 1,440. Therefore, the total number of members at first can be expressed as:

\[
9x + 63 = 1440
\]

Now, solve for \( x \):

\[
9x = 1440 - 63
\]
\[
9x = 1377
\]
\[
x = \frac{1377}{9} = 153
\]

Now that we have \( x = 153 \), we can calculate the number of girls at first:

\[
\text{Number of girls} = 7x = 7 \times 153 = 1071
\]

Thus, there were **1,071 girls** in the swimming club at first.

Would you like further details on any part of this solution, or do you have any questions?

Here are some related questions:
1. How many boys were in the swimming club at first?
2. What percentage of the total members were girls at first?
3. If 30 more boys joined the club, what would the new ratio of girls to boys be?
4. If the ratio of new members who joined was 5:4 (girls to boys), how many girls joined?
5. How would the problem change if there were 100 fewer members after the new members joined?

**Tip:** Ratios can be scaled by multiplying both terms by the same number to maintain their proportionality!

The ratio of the number of girls to the number of boys in a swimming club was 7 : 2 at first. When 63 new members joined the club, the total number of members in the swimming club became 1,440. How many girls were in the swimming club at first?

Learn how to solve a ratio problem involving a swimming club where the initial ratio of girls to boys is 7:2. When 63 new members join, the total membership reaches 1,440. This step-by-step solution explains how to find the number of girls at first using algebraic methods. Ideal for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation