https://file.aiquickdraw.com/mathbot/file/1730566030577umme0r7q.jpg

Please use algebra to solve this question

Let's solve this problem using algebra.

Let's denote:
- \( x \) as the total number of children initially invited to the party.

### Step-by-Step Solution

1. **Sweets Prepared Per Child**:
   Cindy prepared 8 sweets for each child initially invited to the party. Therefore, the total number of sweets Cindy prepared would be:
   \[
   8x
   \]

2. **Effect of Absent Children**:
   Since 3 children were absent, the number of children who actually attended the party is:
   \[
   x - 3
   \]

3. **Additional Sweets Per Child**:
   Each of the children who attended received 4 extra sweets in addition to the 8 sweets initially prepared for them. So, each child who attended received a total of:
   \[
   8 + 4 = 12 \text{ sweets}
   \]

4. **Total Sweets Calculation**:
   The total number of sweets distributed to the children who attended is:
   \[
   12(x - 3)
   \]

5. **Setting Up the Equation**:
   Since the total sweets Cindy prepared is the same as the total sweets distributed, we can set up the equation:
   \[
   8x = 12(x - 3)
   \]

6. **Solving for \( x \)**:
   Expanding and simplifying the equation:
   \[
   8x = 12x - 36
   \]
   Subtract \( 8x \) from both sides:
   \[
   0 = 4x - 36
   \]
   Add 36 to both sides:
   \[
   36 = 4x
   \]
   Divide by 4:
   \[
   x = 9
   \]

7. **Total Sweets Prepared**:
   Now that we know \( x = 9 \), we can calculate the total sweets Cindy prepared:
   \[
   8x = 8 \times 9 = 72
   \]

### Answer
Cindy prepared a total of **72 sweets**.

Would you like further clarification on any steps?

### Related Questions:
1. What if Cindy prepared 10 sweets per child instead of 8?
2. How many sweets would each child receive if only 2 children were absent?
3. If Cindy wanted each child to get 15 sweets, how many would she need to prepare initially?
4. How would the equation change if 5 children were absent instead of 3?
5. What if each attending child received 3 extra sweets instead of 4?

### Tip:
Setting up an equation based on the problem’s conditions is a powerful approach in algebra, especially for problems involving totals or distributions.

Cindy prepared 8 sweets for each child at a party. As 3 children were absent from the party, each of the remaining children shared 4 more sweets. How many sweets did Cindy prepare?

Find out how to determine the total number of sweets Cindy prepared for a party. This problem uses algebra to solve a real-life distribution scenario, calculating based on 8 sweets per child and additional sweets due to absences. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation