Question

A concert promoter needs to make $63,600 from the sale of 1720 tickets. The promoter charges $30 for some tickets and $50 for the others. Let x represent the number of $30 tickets and y represent the number of $50 tickets. (a) Write an equation that states that the sum of the tickets sold is 1720. Correct: Your answer is correct. (b) Write a formula for how much money is received from the sale of $30 tickets? $ Incorrect: Your answer is incorrect. (c) Write a formula for how much money is received from the sale of $50 tickets? $ Incorrect: Your answer is incorrect. (d) Write an equation that states that the total amount received from the sale is $63,600. Correct: Your answer is correct. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $63,600. x = 1120 Correct: Your answer is correct. y = 600 Correct: Your answer is correct.

Answer 1

• x + y = 1720
• Total money received = 30(x)
• Total money received = 50(y)
• 30(x) + 50(y) = 63,600
• Number of y ticket = 600
• Number of x ticket = 1,120

Explanation:

Given:

Total amount need = $63,600

Ticket cost (x) = $30 each

Ticket cost (y) = $50 each

Number of total ticket = 1720

Computation:

1. Sum of total ticket sold

x + y = 1720

2. Formula for sale of $30 ticket

Total money received = 30(x)

3. Formula for sale of $50 ticket

Total money received = 50(y)

4. Equation for total amount received

30(x) + 50(y) = 63,600

5. Number of each ticket

x + y = 1720 ..........Eq1

30(x) + 50(y) = 63,600.........Eq2

Eq 1 × 30

30(x) + 30(y) = 51,600.........Eq3

From Eq2 - Eq3

20y = 12,000

y = 600

Number of y ticket = 600

Number of x ticket = 1720 - 600

Number of x ticket = 1,120