Question

A jazz concert brought in $159,000 on the sale of 7600 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?

Answer 1

Answer: 5,800 $15 tickets, 1,800 $25 tickets

Explanation

x= the first type of ticket
y= second type of ticket

First add x and y to equal total of tickets.

x+y= 7600

Next add 15x and 25y to equal total cost.

15x+25y=159,000

So we have
x+y= 7600
15x+25y=159,000

Let’s use the substitution method to get our answers. So lets arrange the equations and different way.

x= 7600-y
15x+25y=159,000

Now let’s substitute the x into the second equation.

15(7600-y)+25y= 159,000 *Distribute 15*

114,000+25y= 159,000 *Subtract
114,000*

25y= 45,000 *Divide 45,000 by 25*

y=1,800

Now let’s replace y with 1,800 to get our x

x+1,800= 7600*Subtract 1,800 from 7,600*

x= 5,800

Hope this helped :3