Question

a concert promoter needs to make $62,100 from the sale of 2500 tickets. the promoter charges $24 for some tickets an use the given information to answer parts (a) through (e).
(a) if there are x of the $24 tickets sold and y of the $45 tickets sold, write an equation that states that the total number o
x + y = 2500
(type an equation.)
(b) how much money is received for the sale of x tickets for $24 each?
$ 24x
(c) how much money is received for the sale of y tickets for $45 each?
$ 45y
(d) write an equation that states that the total amount received from the sale is $62,100.
24x + 45y = 62100
(type an equation. do not include the $ symbol in your answer.)
(e) solve the equations simultaneously to find how many tickets of each type must be sold to yield the $62,100.
$24 tickets and $45 tickets must be sold.

Explanation:

Step1: Isolate x from first equation

From $x + y = 2500$, we get $x = 2500 - y$.

Step2: Substitute x into second equation

Substitute $x = 2500 - y$ into $24x + 45y = 62100$:
$$24(2500 - y) + 45y = 62100$$

Step3: Expand and simplify the equation

$$60000 - 24y + 45y = 62100$$
$$60000 + 21y = 62100$$

Step4: Solve for y

$$21y = 62100 - 60000$$
$$21y = 2100$$
$$y = \frac{2100}{21} = 100$$

Step5: Solve for x using y value

Substitute $y=100$ into $x = 2500 - y$:
$$x = 2500 - 100 = 2400$$

Answer:

2400 $24 tickets and 100 $45 tickets must be sold.