The admission fee at a local zoo is
$1.50 for children and
$4.00 for adults. On a certain day,
2200 people enter the zoo and
$4,550.00 is collected. How many children and how many adults attended?
c = children
a = adults
2200 people enter the zoo mean :
c + a = 2200
$4,550.00 is collected mean :
1.5 c + 4 a = 4550
Now you must solve system:
c + a = 2200
1.5 c + 4 a = 4550
c + a = 2200 Subtract c to both sides
c + a - c = 2200 - c
a = 2200 - c
1.5 c + 4 a = 4550
1.5 c + 4 ( 2200 - c ) = 4550
1.5 * c + 4 * 2200 - 4 c = 4550
1.5 * c + 8800 - 4 c = 4550
- 2.5 c + 8800 = 4550 Subtract 8800 to both sides
- 2.5 c + 8800 - 8800 = 4550 - 8800
- 2.5 c = - 4250 Divide both sides by - 2.5
c = - 4250 / - 2.5
c = 1700
a = 2200 - c = 2200 - 1700 = 500
1700 children and 500 adults
Proof :
c + a = 1700 = 2200
$ 1.5 * c + $ 4 * a =
$ 1.5 * 1700 + $ 4 * 500 =
$ 2550 + $ 2000 = $ 4550
Thank you.
To solve this problem, we can use a system of equations. Let's assume that the number of children attending is represented by "c" and the number of adults attending is represented by "a."
We can set up two equations to represent the given information:
c + a = 2200 (Equation 1) -- This equation represents the total number of people attending the zoo.
1.50c + 4.00a = 4550 (Equation 2) -- This equation represents the total amount of money collected.
To solve this system of equations, we can use either substitution or elimination method. Let's use substitution method:
From Equation 1, we can rewrite it as c = 2200 - a.
Now we will substitute this expression for "c" in Equation 2:
1.50(2200 - a) + 4.00a = 4550
Expand and simplify:
3300 - 1.50a + 4.00a = 4550
2.50a = 4550 - 3300
2.50a = 1250
Divide both sides by 2.50:
a = 500
Now we substitute this value back into Equation 1 to find the value of "c":
c + 500 = 2200
c = 2200 - 500
c = 1700
Therefore, there were 1700 children and 500 adults who attended the zoo on that day.
c+a = 2200
1.50c + 4.00a = 4550.00