SOLUTION: Formulate a system of equations for the situation below and solve. A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Formulate a system of equations for the situation below and solve. A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a       Log On


   

Question 1107238: Formulate a system of equations for the situation below and solve.
A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $5200. How many children attended the show?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
students x
adults a
children c

system%28x%2Ba%2Bc=900%2Ca=%28x%2Bc%29%2F2%2C4c%2B6x%2B8a=5200%29

Question is to solve for c.

system%284c%2B6x%2B8a=5200%2Cx%2Ba%2Bc=900%2C2a=x%2Bc%2Cx=2a-c%29

system%282c%2B3%282a-c%29%2B4a=2600%2C%282a-c%29%2Ba%2Bc=900%29

system%282c%2B6a-3c%2B4a=2600%2C3a=900%29

system%2810a-c=2600%2Ca=300%29

3000-c=2600

c=3000-2600

highlight%28c=400%29