The admission fee at a small fair is $3 for children and $4.50 for adults. On Sunday, 1000 people went to the fair and $4050 were raised. How many children and

Question

Systems of Equations.

Answer 1

Let x = the number of adults who went to the fair. Since 1000 people attended in total, the number of children who attended is 1000-x.

 

Revenue = (Price per adult)*(Number of adults) + (Price per child)*(Number of children)

 

$4050 = ($4.50)*(x) + ($3.00)*(1000-x)

 

4050 = 4.5x + 3000 - 3x

 

1050 = 1.5x

 

700 = x (the number of adults)

 

The number of children is 1000-700 = 300

Answer 2

Let C denote the #ofChildren and A the #ofAdults...

 

Then 4050=3C+4.50A...and 1000=C+A based on attendance.

 

Use your favorite method of solving linear equations!

 

Substitute one equation into the other, Multiply and add, graph and find intersection of lines, use matrix algebra...there are a litany of ways to solve this system, now that it is expressly written as two lines in the A/C plane.