Admission to a baseball game is $3.00 for general admission and $5.00 for reserved seats. The receipts were $4545.00 for 1285 paid admissions. How many of each ticket were sold?

Question

Admission to a baseball game is $3.00 for general admission and $5.00 for reserved seats. The receipts were $4545.00 for 1285 paid admissions. How many of each ticket were sold?

Answer 1

number of general --- x

number of reserved --- 1285-x

3x + 5(1285-x) = 4545

solve for x and state conclusion

Answer 2

Well, it seems like we have a case of baseball ticket madness! Let's solve this mystery together.

Let's assume the number of general admission tickets sold is X, and the number of reserved seats sold is Y.

According to the information given, each general admission ticket costs $3.00, and each reserved seat ticket costs $5.00. So we can create two equations from this:

Equation 1: X + Y = 1285 (since the total number of tickets sold is 1285)
Equation 2: 3X + 5Y = 4545 (since the total receipts were $4545.00)

Now, we can use some clever detective work to find the values of X and Y. Let's solve this using the elimination method.

Multiplying Equation 1 by 3, we get:
3X + 3Y = 3855

Now let's subtract Equation 2 from this:
(3X + 3Y) - (3X + 5Y) = 3855 - 4545

Simplifying:
-2Y = -690
Y = 345

Now that we know the value of Y, we can substitute it back into Equation 1:
X + 345 = 1285
X = 940

Ta-da! We've cracked the case! It turns out that 940 general admission tickets and 345 reserved seat tickets were sold.

Answer 3

Let's solve this step-by-step:

Step 1: Assign variables.
Let's assume the number of general admission tickets sold as "x" and the number of reserved seat tickets sold as "y".

Step 2: Write the equations.
From the given information, we can set up two equations:
Equation 1: x + y = 1285 (total number of paid admissions)
Equation 2: 3x + 5y = 4545 (total amount of receipts)

Step 3: Solve the equations.
To solve the system of equations, we can use the substitution method.

From Equation 1, we can express x in terms of y:
x = 1285 - y

Substitute this value of x into Equation 2:
3(1285 - y) + 5y = 4545

Simplify the equation:
3855 - 3y + 5y = 4545
2y = 690
y = 345

Step 4: Find x.
Substitute the value of y into Equation 1:
x + 345 = 1285
x = 1285 - 345
x = 940

Step 5: Check the solution.
Now we can check if the solution satisfies both equations:
Equation 1: 940 + 345 = 1285 (valid)
Equation 2: 3(940) + 5(345) = 4545 (valid)

Step 6: Answer the question.
So, 940 general admission tickets and 345 reserved seat tickets were sold.

Answer 4

To determine the number of tickets sold for each type, general admission and reserved seats, we can set up a system of equations.

Let's assume that x represents the number of general admission tickets sold, and y represents the number of reserved seats tickets sold.

The total number of tickets sold can be represented as:
x + y = 1285 (Equation 1)

The total revenue from the ticket sales can be represented as:
3x + 5y = 4545 (Equation 2)

We now have a system of equations. To solve these equations, we can use a method called substitution.

Step 1: Solve Equation 1 for x in terms of y:
x = 1285 - y

Step 2: Substitute the value of x in Equation 2:
3(1285 - y) + 5y = 4545

Step 3: Distribute and simplify:
3855 - 3y + 5y = 4545
2y = 4545 - 3855
2y = 690
y = 690 / 2
y = 345

Step 4: Substitute the value of y back into Equation 1 to solve for x:
x + 345 = 1285
x = 1285 - 345
x = 940

Therefore, 940 general admission tickets and 345 reserved seat tickets were sold.