Which system of equations can be used to find the price in dollars of an adult ticket, x, and a student ticket, y?
Understand the Problem
The question is asking for the correct system of equations that represents the situation of a youth group visiting a museum, which involves calculating the prices of adult and student tickets based on given total costs for different groups.
Answer
A: $$ 3x + 2y = 102 $$ $$ 6x + 7y = 95 $$
Answer for screen readers
The correct system of equations representing the situation is:
- ( 3x + 6y = 102 )
- ( 2x + 7y = 95 )
So, the answer is A:
$$ 3x + 2y = 102 $$
$$ 6x + 7y = 95 $$
Steps to Solve
-
Identify variables and set up the equations
Let $x$ be the price of an adult ticket and $y$ be the price of a student ticket. The problem states two scenarios with specific totals. -
Construct the first equation
For the first scenario, three adults and six students paid $102:
$$ 3x + 6y = 102 $$ -
Construct the second equation
For the second scenario, two adults and seven students paid $95:
$$ 2x + 7y = 95 $$ -
Simplifying the equations
From the first equation, we can divide all terms by 3 to simplify: $$ x + 2y = 34 $$
From the second equation, divide all terms by 2 to simplify further: $$ x + \frac{7}{2}y = 47.5 $$
The correct system of equations representing the situation is:
- ( 3x + 6y = 102 )
- ( 2x + 7y = 95 )
So, the answer is A:
$$ 3x + 2y = 102 $$
$$ 6x + 7y = 95 $$
More Information
This problem requires formulating systems of equations based on real-world scenarios involving ticket prices, which is a common application of algebra in word problems.
Tips
- Mislabeling the variables, such as confusing adult and student ticket prices.
- Incorrectly setting up the equations when reading the problem, which can lead to wrong total amounts.
- Forgetting to simplify equations properly when trying to work with them.
