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?

To solve the problem, let's denote the number of girls and boys in the swimming club initially as follows:

- Let the number of girls be \(7x\).
- Let the number of boys be \(2x\).

According to the problem, the total number of members after 63 new members joined is 1,440.

**Step 1: Write down the equation for the initial total number of members:**

\[
\text{Initial total number of members} = 7x + 2x = 9x
\]

**Step 2: Consider the addition of new members:**

The number of new members added is 63, so the total number of members after the new members joined is:

\[
9x + 63 = 1440
\]

**Step 3: Solve for \(x\):**

First, subtract 63 from both sides of the equation:

\[
9x = 1440 - 63
\]

\[
9x = 1377
\]

Now, divide both sides by 9:

\[
x = \frac{1377}{9} = 153
\]

**Step 4: Calculate the number of girls initially:**

The initial number of girls is \(7x\):

\[
7x = 7 \times 153 = 1071
\]

Thus, the initial number of girls in the swimming club was **1,071**.

Would you like further details, or do you have any questions?

Here are five related questions you might find interesting:
1. If the ratio had been 5:3 instead, how many girls would there have been initially?
2. How many boys were initially in the swimming club?
3. What would the total number of members be if another 100 members joined after the first 63?
4. How would the initial ratio change if 50 girls left the club?
5. If the total number of members after 63 joined had been 1,500 instead of 1,440, how would that affect the initial number of girls?

**Tip:** Always double-check your calculations when solving word problems to avoid small mistakes that can lead to incorrect answers.

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?

Discover how to find the initial number of girls in a swimming club given the ratio of girls to boys and the total members after new members joined. This detailed solution covers algebraic concepts and is suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation