Question

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.


step 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.

step B. Solve the system you wrote in part (a) using the substitution method. Show your work.

step C. Interpret your solution in the context of the problem.

Please explain your answer for brainliest.

Answer 1

Answer:

The number of adults attending the zoo is 12, and the number of children attending is 17.

Step-by-step explanation:

Let $a$ be the number of adults, and $c$ be the number of children attending the zoo, then system representing the situation is

(1). $10a+6c=222$         (this says that the total cost of the tickets is $222)

(2). $a+c=29$               (this says that a total of 29 people attended the zoo)

We solve this system by solving for $a$ in equation (2), and substituting that into equation (1) as follows:

$a =29-c$

$10(29-c)+6c = 222$

expand and get

$290-10c+6c=222$

$290-4c=222$

solving for $c$ we get:

$\boxed{ c=17}$

Now we put this value of $c$ into equation (2), and solve for $a$ :

$a+ 17 =29$

$\boxed{ a= 12}$

Thus, the number of adults attending the zoo is 12, and the number of children attending is 17.