Formulate a system of equations and solve.

Question

A theater has a seating capacity of 711 and charges $2 for children, $4 for students, and $6 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $2810. How many children attended the show?

Answer 1

A theater has a seating capacity of 711

no. of children =x

no. of students =y

no. of adults =z.

 

At a certain screening with full attendance, there were half as many adults as children and students combined.
The receipts totaled $2810
How many children attended the show?

Equations:

People: x + y + z = 711

Quantity: z = (1/2)(x+y)

Values: 2x + 4y + 6z =2810

 

Rearrange:

 

x + y + z = 711
x + y -2z = 0
x +2y +3z = 1405

 

solving these 3 equations(by elimination and substitution or any method)
x = 254
y = 220
z = 237

 

Total children attended show =254