at a museum, adult admission is $15. and children admissions is $6.50. during one day, a total of 2300 adult and children admissions were collected, and $27,700 was collected in fees. how many adult admissions were collected?

To expand on the previous response,

you have to solve through a system of equations:

a + c = 2300
15a + 6.5c = 27700

In the first equation, solve for C:

c = 2300 - a

Then substitute into the second equation:

15a + 6.5(2300 - a) = 27700

15a + 14950 - 6.5a = 27700

15a - 6.5a = 27700 - 14950

8.5a = 12750

8.5a/8.5 = 12750/8.5

a = 1500

Therefore, 1500 adult admissions were collected.

You can also substitute a = 1500 into the first equation:

c = 2300 - 1500
c = 800 children admissions sold.

Verify,

a + c = 2300

1500 + 800 = 2300 total admissions.

Best,
Farohw

Let's assume the number of adult admissions is A.

The number of children admissions is C.
According to the given information, the adult admission fee is $15 and the children's admission fee is $6.50.
So, the total revenue from adult admissions is 15A and the total revenue from children admissions is 6.50C.
The total number of admissions is 2300, so we can write this as:
A + C = 2300 ...(Equation 1)
The total revenue collected is $27,700, so we can write this as:
15A + 6.50C = 27700 ...(Equation 2)

Now we can solve these two equations to find the values of A and C.
We can multiply Equation 1 by 6.50 to make the coefficients of C the same in both equations:
6.50A + 6.50C = 14950 ...(Equation 3)

Subtract Equation 3 from Equation 2 to eliminate C:
15A + 6.50C - (6.50A + 6.50C) = 27700 - 14950
8.5A = 12750

Divide both sides of the equation by 8.5:
A = 1500

Therefore, the number of adult admissions collected is 1500.

To find the number of adult admissions collected, we need to set up a system of equations based on the information given.

Let's assume the number of adult admissions collected is "A" and the number of child admissions collected is "C."

From the information given, we can set up the following equations:
Equation 1: A + C = 2300 (Total number of adult and child admissions collected)
Equation 2: 15A + 6.50C = 27700 (Total fees collected)

Now we can use these equations to solve for the number of adult admissions collected.

To solve the system of equations, we can use the method of substitution or elimination.
Let's use the substitution method.

Step 1: Solve Equation 1 for A in terms of C.
A = 2300 - C

Step 2: Substitute the value of A in Equation 2 with 2300 - C.
15(2300 - C) + 6.50C = 27700

Step 3: Distribute and simplify.
34500 - 15C + 6.50C = 27700
-8.50C = -6800

Step 4: Divide by -8.50 to solve for C.
C = -6800 / -8.50
C ≈ 800

Step 5: Substitute the value of C back into Equation 1 to find A.
A + 800 = 2300
A = 2300 - 800
A = 1500

Therefore, there were 1500 adult admissions collected at the museum.

The algebra for this would be:

15a + 6.5c = 27700

where a is the number of adults and c is the number of children.