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Answer :
Final answer:
The price of a senior citizen ticket is approximately $11.23 and the price of a student ticket is approximately $24.24.
Explanation:
Let's denote the price of a senior citizen ticket as x and the price of a student ticket as y.
From the given information, we can form two equations:
11x + 2y = 172 (Equation 1)
9x + 8y = 198 (Equation 2)
We can solve this system of equations by elimination or substitution. Let's solve it by elimination:
Multiplying Equation 1 by 4 and Equation 2 by 2, we have:
44x + 8y = 688 (Equation 3)
18x + 16y = 396 (Equation 4)
Now, subtracting Equation 4 from Equation 3, we get:
26x = 292
Dividing both sides by 26, we find:
x = 11.23
Substituting the value of x into Equation 1, we can solve for y:
11(11.23) + 2y = 172
123.53 + 2y = 172
Subtracting 123.53 from both sides, we get:
2y = 48.47
Dividing both sides by 2, we find:
y ≈ 24.24
Therefore, the price of a senior citizen ticket is approximately $11.23 and the price of a student ticket is approximately $24.24.
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