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.
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.
a+c = 29
10a+6c = 222
...
To write a system of equations to represent the situation, we can use the information given in the problem.
Let a represent the number of adult admissions.
Let c represent the number of child admissions.
The first equation represents the total number of tickets purchased:
a + c = 29
The second equation represents the total amount paid for admission fees:
10a + 6c = 222
Now let's solve this system using the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for a in terms of c:
a = 29 - c
Step 2: Substitute the value of a in terms of c into the second equation:
10(29 - c) + 6c = 222
Step 3: Distribute the 10:
290 - 10c + 6c = 222
Step 4: Combine like terms:
-4c + 290 = 222
Step 5: Move the constant term to the right side by subtracting 290 from both sides:
-4c = 222 - 290
-4c = -68
Step 6: Divide both sides by -4 to solve for c:
c = -68 / -4
c = 17
Step 7: Now substitute the value of c into the first equation to solve for a:
a + 17 = 29
a = 29 - 17
a = 12
So, the solution to the system of equations is a = 12 and c = 17.
In the context of the problem, this means that there were 12 adult admissions and 17 child admissions.