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 $1694 From a total of 108 youths and adults . How many admissions of each type were sold?

y + a = 108

14.5 y + 18.5 a = 1694

solve the system for y and a

multiplying by 14.5 ... 14.5 y + 14.5 a = 14.5 * 108

subtract equations to eliminate y

solve for a , then substitute back to find y

To solve this problem, let's denote the number of youth admissions as 'y' and the number of adult admissions as 'a'. We can set up two equations based on the given information:

1. The total amount collected from youth admissions is $14.50 multiplied by the number of youth admissions, which is y:
Total collected from youth = $14.50 * y

2. The total amount collected from adult admissions is $18.50 multiplied by the number of adult admissions, which is a:
Total collected from adults = $18.50 * a

We are also given that the total amount collected from both youth and adult admissions is $1694:
Total collected = $14.50 * y + $18.50 * a

Now, we can set up the equation based on the total admission count of 108 people:
Total admissions = y + a = 108

To find the number of admissions of each type, we need to solve this system of equations. Let's substitute the value of y from the third equation into the second equation:

108 - a + a = 108

Simplifying:
1a = 0

This means that a has no effect on the equation, and we cannot determine its value independently. However, we can find the value of y by substituting it into one of the original equations. Let's use the equation for the total amount collected:

$14.50 * y + $18.50 * a = $1694

Substituting a = 108 - y:

$14.50 * y + $18.50 * (108 - y) = $1694

Expanding and simplifying:

$14.50 * y + $18.50 * 108 - $18.50 * y = $1694

$14.50 * y - $18.50 * y + $18.50 * 108 = $1694

Combining like terms:

$4 * y = $1694 - $18.50 * 108

$4 * y = $1694 - $1998

$4 * y = -$304

y = -$304 / $4

y ≈ -76 (This is not a possible number of youth admissions)

Based on the calculations, we have encountered a contradiction. The number of youth admissions cannot be negative. Thus, there seems to be an error or inconsistency in the given information or the problem statement.