A museum charges ​$13.50 for a​ one-day youth admission and ​$16.50 for a​ one-day adult admission. One​ Friday, the museum collected ​$1581 from a total of 110 youths and adults. How many admissions of each type were​ sold?

same type of problem as your previous post ....

students --- x
adults ----- y

x+y = 110 ---> y = 110-x
13.5x + 16.5y = 1581

sub the first into the second:
13.5x + 16.5(110-x) = 1581
13.5 + 1815 - 16.5x = 1581
-3x = -234
x = 78

So 78 students and 32 adults

To solve this problem, let's use a system of equations.

Let's represent the number of youth admissions as "y" and the number of adult admissions as "a".

According to the given information, the museum collected $1581, so we can write the first equation as:
13.50y + 16.50a = 1581

We also know that the total number of admissions (youth and adults) is 110, so the second equation is:
y + a = 110

Now we can solve these equations using substitution or elimination method.

Let's use the substitution method. Solve the second equation for "y":
y = 110 - a

Now substitute this value of "y" in the first equation:
13.50(110 - a) + 16.50a = 1581

Expand the equation:
1485 - 13.50a + 16.50a = 1581

Combine like terms:
1485 + 3a = 1581

Subtract 1485 from both sides:
3a = 96

Divide both sides by 3:
a = 32

Now we know that there were 32 adult admissions. We can substitute this value back into the second equation to find the number of youth admissions:
y + 32 = 110
y = 110 - 32
y = 78

So, there were 78 youth admissions and 32 adult admissions sold.

Let's denote the number of youth admissions as y and the number of adult admissions as a.

According to the given information, the total revenue from youth admissions is $13.50 multiplied by the number of youth admissions, which can be written as 13.50y.

Similarly, the revenue from adult admissions is $16.50 multiplied by the number of adult admissions, which can be written as 16.50a.

We also know that the total revenue collected is $1581, so we can set up the equation:

13.50y + 16.50a = 1581

Now, let's consider the number of admissions. The total number of admissions is 110, so we can write another equation:

y + a = 110

To solve these equations together, we can use substitution or elimination method.

Let's use the elimination method:

Multiply the second equation by -13.50 to make the coefficients of y the same:

-13.50y - 13.50a = -1485

Now, we can add the two equations:

(13.50y + 16.50a) + (-13.50y - 13.50a) = 1581 - 1485

This simplifies to:

3a = 96

Divide both sides by 3:

a = 32

Now, substitute this value back into the second equation to find the value of y:

y + 32 = 110

y = 110 - 32

y = 78

Therefore, there were 78 youth admissions and 32 adult admissions sold.