Admission to a zoo costs $10 for adults and $6 for children. A group of 29 people attending the zoo paid a total of $222 in admission fees.
a. Write a system of equations to represent the situation. Let a represent the number of adult admissions, and let c represent the number of child admissions.
Solve the system you wrote in part (a) using the substitution method. Show your work.
Interpret your solution in the context of the problem
PLEASE HELP IM SO LOST
count the people and the money:
a+c = 29
10a+6c = 222
Now finish it off
thank you oobleck!
To solve this problem, we can set up a system of equations using the given information.
Let's use the variables "a" to represent the number of adult admissions and "c" to represent the number of child admissions.
1. The cost for adults is $10 per person, so the total cost for adult admissions would be 10a.
2. The cost for children is $6 per person, so the total cost for child admissions would be 6c.
3. The total number of people attending the zoo is given as 29, so the sum of adult and child admissions should be equal to 29: a + c = 29.
4. The total admission fee collected is given as $222: 10a + 6c = 222.
Now, we have the following system of equations:
Equation 1: a + c = 29
Equation 2: 10a + 6c = 222
To solve this system using substitution method, we can solve one equation for one variable and substitute it into another equation. Let's solve Equation 1 for a:
From Equation 1:
a = 29 - c
Substitute this value of a into Equation 2:
10(29 - c) + 6c = 222
290 - 10c + 6c = 222
290 - 4c = 222
Now, let's isolate the variable "c" by moving constants to the other side:
-4c = 222 - 290
-4c = -68
Divide by -4 on both sides to solve for c:
c = -68 / -4
c = 17
Now, we can substitute the value of c back into Equation 1 to solve for a:
a + 17 = 29
a = 29 - 17
a = 12
So, there were 12 adult admissions and 17 child admissions.
Interpretation:
The solution tells us that there were 12 adults and 17 children attending the zoo. The adult admissions at $10 each would contribute $120 (12 * 10) to the total admission fee, while the child admissions at $6 each would contribute $102 (17 * 6). So, the total admission fees collected equals $222, as stated in the problem.