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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.

Answer :

calculista

Answer:

The number of adult admissions was 12 and the the number of child admissions was 17

Step-by-step explanation:

Let

a ----> represent the number of adult admissions

c ----> represent the number of child admissions

we know that

A group of 29 people attending the zoo paid a total of $222 in admission fees

so

[tex]a+c=29[/tex]

[tex]a=29-c[/tex] ----> equation A

[tex]10a+6c=222[/tex] ----> equation B

Solve using the substitution method

substitute equation A in equation B

[tex]10(29-c)+6c=222[/tex]

solve for c

[tex]290-10c+6c=222\\4c=68\\c=17[/tex]

Find the value of a

[tex]a=29-17=12[/tex]

therefore

The number of adult admissions was 12 and the the number of child admissions was 17

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