Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The Family Arts Center charges $21 for adults, $13 for senior citizens, and $7 for children under 12 fortheir live performances on Sunday afternoon. This past Sunday, the paid revenue was $10,690 for 806tickets sold. There were 44 more children than adults. How many children attended?
A)282 children
B)238 children
C)286 children
D)272 children

Question

Quizplus · Accepted Answer

Let A be the number of adults, S be the number of senior citizens, and C be the number of children. We have the following equations based on the problem:  1) A + S + C = 806  2) 21A + 13S + 7C = 10,690  3) C = A + 44  Substitute C = A + 44 into the first equation:  A + S + (A + 44) = 806  2A + S = 762  Now substitute C = A + 44 into the second equation:  21A + 13S + 7(A + 44) = 10,690  21A + 13S + 7A + 308 = 10,690  28A + 13S = 10,382  Now solve the system of equations:  2A + S = 762  28A + 13S = 10,382  Multiply the first equation by 13:  26A + 13S = 9,906  Subtract the first equation from the second:  (28A + 13S) - (26A + 13S) = 10,382 - 9,906  2A = 476  A = 238  Now find C:  C = A + 44 = 238 + 44 = 282  So, 282 children attended.

Write the Word or Phrase That Best Completes Each Statement