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.

Question

Mathematics

Nash Barton

17 September, 01:28

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.

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Answers (1)

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Riya Arellano · Answer 1

Number of adults = 12

Number of children = 17

Step-by-step explanation:

Step 1:

Let a be the number of adults and c be the number of children

Given that the total admission fees paid is $222

Cost for adults is $10 and cost for children is $6

So we have,

10 a + 6 c = 222

Step 2:

Total people attending is 29

So, a + c = 29

=> a = 29 - c

Step 3:

Substituting the value for a in the equation in step 1, we have

10 (29-c) + 6 c = 222

290 - 10 c + 6 c = 222

-4 c = 222-290 = - 68

=> c = - 68/-4 = 17

substituting this value of c in the equation in step 2 we have

a = 29 - 17 = 12

So we have 12 adults and 17 children visiting the zoo.