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Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 303 people entered the park, and the admission fees collected totaled 792.00 dollars. How many children and how many adults were admitted?

Answer 1

PROBLEM

 

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 303 people entered the park, and the admission fees collected totaled 792.00 dollars. How many children and how many adults were admitted?

 

SOLUTION

 

LET C BE THE NUMBER OF CHILDREN AND A BE THE NUMBER OF ADULTS

 

SO, EQUATION FOR THE NUMBER OF PEOPLE: C + A = 303

 

AND EQUATION FOR THE ADMISSION FEES: 1.5*C + 4*A = 792

 

MULTIPLY THE PEOPLE EQUATION BY -4 SO YOU CAN ELIMINATE A, THEREFORE

 

     -4 ( C + A = 303) BECOMES   -4*C -  4*A = - 1212

                                               1.5*C + 4*A =     792

                                              -2.5*C           = -  420

                                                               C  =    168

 

SUBSTITUTE THE VALUE FOR C INTO THE EQUATION FOR PEOPLE:     168 + A = 303; A = 303 - 168, A = 135

 

THEREFORE, 168 CHILDREN WERE ADMITTED AND 135 ADULTS WERE ADMITTED.

 

Answer 2

c = number of children admitted at $1.50 each

 

303 - c = number of adults admitted at $4.00 each

 

($1.50)c + ($4.00)(303 - c) = $792.00

 

Solve for c.

 

-2.5c = -420

 

c = 168

 

168 children were admitted.

 

135 adults were admitted (i.e. 303 - 168)

 

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