Answer:
So, the price of the buffet for an adult is $11.65 and for a child is $8.55.
Step-by-step explanation:
Let's denote the price for an adult's buffet lunch as \( A \) and the price for a child's buffet lunch as \( C \).
We have two equations based on the given information:
1. For the Jung group:
\[ 2A + 3C = 48.95 \]
2. For the Harvey group:
\[ 3A + 2C = 52.05 \]
We can solve this system of linear equations to find the values of \( A \) and \( C \).
Multiplying the first equation by 3 and the second equation by 2, we get:
1. \( 6A + 9C = 146.85 \)
2. \( 6A + 4C = 104.10 \)
Now, subtract the second equation from the first to eliminate \( A \):
\[ (6A + 9C) - (6A + 4C) = 146.85 - 104.10 \]
\[ 5C = 42.75 \]
\[ C = \frac{42.75}{5} = 8.55 \]
Now, substitute the value of \( C \) into one of the original equations to find \( A \). Let's use the first equation:
\[ 2A + 3(8.55) = 48.95 \]
\[ 2A + 25.65 = 48.95 \]
\[ 2A = 48.95 - 25.65 \]
\[ 2A = 23.3 \]
\[ A = \frac{23.3}{2} = 11.65 \]
So, the price of the buffet for an adult is $11.65 and for a child is $8.55.
