Question

A museum charges ​$14.50 for a​ one-day youth admission and ​$18.50 for a​ one-day adult admission. One​ Friday, the museum collected ​$1702 from a total of 108 youths and adults. How many admissions of each type were​ sold?

Answer 1

Answer: 74 youth tickets and 34 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of one-day youth admission tickets sold.

Let y represent the number of one-day adult admission tickets sold.

The total number of youths and adults tickets sold is 108. It means that

x + y = 108

The museum charges ​$14.50 for a​ one-day youth admission and ​$18.50 for a​ one-day adult admission. One​ Friday, the museum collected ​$1702 in total. This means that

14.5x + 18.5y = 1702- - - - - - - - - 1

Substituting x = 108 - y into equation 1, it becomes

14.5(108 - y) + 18.5y = 1702

1566 - 14.5y + 18.5y = 1702

- 14.5y + 18.5y = 1702 - 1566

- 4y = - 136

y = - 136/ - 4

y = 34

x = 108 - 34

x = 74