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A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3147 tickets overall. It has sold 211

more $20 tickets than $10 tickets. The total sales are $61,130. How many tickets of each kind have been sold?
How many $10 tickets were sold?

User Pyroscope
by
8.5k points

2 Answers

2 votes
1040 of $10 tickets were sold
User Dst
by
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7 votes

Answer:

Approximately 1040 of $10 tickets were sold.

Explanation:

Assume the number of $10 tickets sold is "x".

According to the information provided:

The team sells three types of tickets: $10, $20, and VIP ($30).

The total number of tickets sold is 3147.

The team has sold 211 more $20 tickets than $10 tickets.

The total sales are $61,130.

We can set up equations based on the information given:

Total number of tickets sold:

x (number of $10 tickets) + (x + 211) (number of $20 tickets) + (number of VIP tickets) = 3147

Total sales:

$10 * x + $20 * (x + 211) + $30 * (number of VIP tickets) = $61,130

We can solve the equations to find the values of "x" and the number of VIP tickets:

Total number of tickets sold equation:

x + (x + 211) + (number of VIP tickets) = 3147

2x + 211 + (number of VIP tickets) = 3147

2x + (number of VIP tickets) = 3147 - 211

2x + (number of VIP tickets) = 2936

Total sales equation:

$10 * x + $20 * (x + 211) + $30 * (number of VIP tickets) = $61,130

$10 * x + $20x + $20 * 211 + $30 * (number of VIP tickets) = $61,130

$10 * x + $20x + $4220 + $30 * (number of VIP tickets) = $61,130

$30x + $30 * (number of VIP tickets) = $61,130 - $4220

$30x + $30 * (number of VIP tickets) = $56,910

Now, we have a system of two equations:

2x + (number of VIP tickets) = 2936

$30x + $30 * (number of VIP tickets) = $56,910

We can solve this system of equations to find the value of "x" (number of $10 tickets) and the number of VIP tickets. Let's do that:

Solve equation 1 for "number of VIP tickets":

(number of VIP tickets) = 2936 - 2x

Substitute the value of (number of VIP tickets) from equation 1 into equation 2:

$30x + $30 * (2936 - 2x) = $56,910

Now, solve for "x":

$30x + $30 * 2936 - $30 * 2x = $56,910

$30x + $88,080 - $60x = $56,910

-$30x = $56,910 - $88,080

-$30x = -$31,170

Divide both sides by -30:

x = $31,170 / $30

x = 1040.5

Since we can't have half a ticket, let's round down to the nearest whole number:

x ≈ 1040

So, approximately 1040 of $10 tickets were sold.

User Padarom
by
8.7k points