The problem in the image states:

There were 155 people at the basketball game. Tickets for the game are $2.50 for students and $4 for adults. If the total money received for admission was $492.50, how many students and adults attended the game?

Let's solve this step-by-step.

1. Let $x$ represent the number of students and $y$ represent the number of adults.

2. We know:

   • The total number of people: $x + y = 155$
   • The total money received: $2.50x + 4y = 492.50$

Step 1: Set up the system of equations

$x + y = 155$ $2.50x + 4y = 492.50$

Step 2: Solve for one variable

From the first equation, solve for $y$: $y = 155 - x$

Step 3: Substitute into the second equation

Substitute $y = 155 - x$ into the second equation: $2.50x + 4(155 - x) = 492.50$

Step 4: Expand and simplify

$2.50x + 620 - 4x = 492.50$ Combine like terms: $-1.5x + 620 = 492.50$ Subtract 620 from both sides: $-1.5x = -127.50$ Divide by -1.5: $x = 85$

Step 5: Substitute back to find $y$

Substitute $x = 85$ into $y = 155 - x$: $y = 155 - 85 = 70$

Solution

There were 85 students and 70 adults at the game.

Would you like more details, or do you have any questions?

Here are 5 questions that might expand your understanding:

1. How would the solution change if the prices for tickets were different?
2. Can you create a similar problem using different total attendance and ticket prices?
3. How does setting up a system of equations help in solving real-life problems?
4. What if the total money collected was not divisible exactly? How would that affect the solution?
5. Why is it necessary to check the reasonableness of the solution in word problems?

Tip: When solving word problems, always translate the given information into equations that can be solved systematically.