Question

question 1-8
a theater sells tickets for a concert. tickets for lower - level seats sell for $35 each, and tickets for upper - level seats sell for $25 each. the theater sells 350 tickets for $10,250. how many of each type of ticket were sold?
the theater sold lower - level tickets and upper - level tickets
150
200
293
410

Explanation:

Step1: Define variables

Let \( x \) be the number of lower - level tickets and \( y \) be the number of upper - level tickets. We know two equations:

1. The total number of tickets sold: \( x + y=350\), so \( y = 350 - x \)
2. The total revenue from ticket sales: \( 35x+25y = 10250\)

Step2: Substitute \( y \) into the revenue equation

Substitute \( y = 350 - x \) into \( 35x + 25y=10250\):

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Step3: Solve for \( x \)

Subtract 8750 from both sides:

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Divide both sides by 10: \( x=\frac{1500}{10}=150 \)

Step4: Solve for \( y \)

Since \( y = 350 - x \) and \( x = 150 \), then \( y=350 - 150 = 200 \)

Answer:

The theater sold 150 lower - level tickets and 200 upper - level tickets.