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?

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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.