Question

at a local concert, two types of tickets were sold: one for $40 and the other for $60. the sale of 854 tickets generated an amount of $41,240. how many of each kind of tickets were sold?

Explanation:

Step1: Define variables

Let \( x \) be the number of \$40 tickets sold and LXI1 be the number of \$60 tickets sold.
We have two equations:

1. \( x + y = 854 \) (total number of tickets)
2. \( 40x + 60y = 41240 \) (total revenue)

Step2: Solve the first equation for \( x \)

From \( x + y = 854 \), we get \( x = 854 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 854 - y \) into \( 40x + 60y = 41240 \):
\( 40(854 - y) + 60y = 41240 \)
Expand: \( 34160 - 40y + 60y = 41240 \)
Simplify: \( 34160 + 20y = 41240 \)
Subtract 34160 from both sides: \( 20y = 41240 - 34160 = 7080 \)

Step4: Solve for \( y \)

Divide both sides by 20: \( y = \frac{7080}{20} = 354 \)

Step5: Solve for \( x \)

Substitute \( y = 354 \) into \( x = 854 - y \):
\( x = 854 - 354 = 500 \)

Answer:

The number of \$40 tickets sold is 500, and the number of \$60 tickets sold is 354.