A concert hall has 300 seats. If the number of reserved seats is 50 more than th
Practice Questions
Q1
A concert hall has 300 seats. If the number of reserved seats is 50 more than the number of general admission seats, how many reserved seats are there?
125
175
100
150
Questions & Step-by-Step Solutions
A concert hall has 300 seats. If the number of reserved seats is 50 more than the number of general admission seats, how many reserved seats are there?
Step 1: Understand that there are two types of seats: general admission seats and reserved seats.
Step 2: Let the number of general admission seats be represented by the letter 'x'.
Step 3: Since the number of reserved seats is 50 more than the general admission seats, we can express the reserved seats as 'x + 50'.
Step 4: The total number of seats in the concert hall is 300. Therefore, we can write the equation: x (general admission) + (x + 50) (reserved) = 300.
Step 5: Simplify the equation: x + x + 50 = 300, which becomes 2x + 50 = 300.
Step 6: To solve for 'x', first subtract 50 from both sides of the equation: 2x = 300 - 50, which simplifies to 2x = 250.
Step 7: Now, divide both sides by 2 to find 'x': x = 250 / 2, which gives x = 125.
Step 8: Now that we know the number of general admission seats (x = 125), we can find the number of reserved seats by calculating x + 50: 125 + 50 = 175.
Step 9: Therefore, the number of reserved seats is 175.
Algebraic Equations – The question tests the ability to set up and solve a linear equation based on a word problem.
Word Problems – The question requires translating a real-world scenario into a mathematical equation.
Understanding Relationships – The question involves understanding the relationship between reserved and general admission seats.
