Intermediate Algebra Question

Question

at a museum adult admission is 13 and children admission is 7. During one day, a total of 1900 adult and children admissions were collected and 21,700 in admission fees was collected. How many adult admissions were collected?

Answer 1

The total admissions (T) is equal to the number of adult admissions (A) plus the number of child admissions (C) so if:

A = # of Adult Admissions    and

C = # of Child Admissions    and

1900 = Total # of Admissions then

 

A + C = 1900

 

Also the total paid for adult Admissions ( Pa = 13 * A) plus the total paid for child admissions (Pc = 7 * C) is equal to the total admission collected (21,700).

 

13A + 7C = 21,700.

 

Therefore you can solve the system of equations for A & C and the answer is A.

 

    A  +     C    =    1900

13A  +     7C   =    21,700

 

Use ellimination method by adding -7 times the first equation to the 2nd equation to get

 

6A = 8400

 

Divide both sides by 6 and get

 

A = 1400.

 

so 1400 adult admissions were sold.