The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, $5,050 is collected. If 1,000 adults attended the fair, write and solve a linear equation to find the number of children that attended. Ax+By=C

Let's define the variables as follows:
- Let $ x $ represent the number of children who attended the fair.
- The number of adults who attended is given as 1,000.

We know that:
- The admission fee for children is $1.50, so the total amount collected from children is $ 1.50x $.
- The admission fee for adults is $4.00, and the total amount collected from 1,000 adults is $ 4.00 \times 1000 = 4000 $.

The total amount collected from both children and adults is $5,050. Therefore, we can write the equation:
\[
1.50x + 4000 = 5050
\]

### Solving the equation:
1. Subtract 4000 from both sides:
\[
1.50x = 5050 - 4000
\]
\[
1.50x = 1050
\]

2. Divide both sides by 1.50:
\[
x = \frac{1050}{1.50}
\]
\[
x = 700
\]

Thus, 700 children attended the fair.

### The linear equation is:
\[
1.50x + 4 \times 1000 = 5050
\]

Would you like more details or have any questions?

---

Here are 5 related questions you can explore:
1. What if 1,200 adults attended the fair? How would the equation change?
2. How much would the total collection be if the admission fees were increased by 20%?
3. How many adults and children attended if the total collected was $6,000?
4. What if children were charged $2.00 per ticket? How many children would have attended then?
5. How would the number of children change if fewer adults attended the fair?

**Tip:** When solving linear equations, it's often helpful to first isolate the variable by eliminating constants and coefficients through basic operations like addition, subtraction, multiplication, or division.

Discover how to solve a linear equation to find the number of children who attended a fair, where $5,050 was collected from $1.50 child tickets and $4.00 adult tickets. This algebraic problem is ideal for students in 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