How would I solve this?ASB sells tickets to a dance for $10 to students who have an ASB sticker and $12 to those who don't have an ASB sticker. 160 tickets are sold and $1720 is raised. How many of each are sold?

1 Answer
Oct 28, 2017

Answer:

#60# people without an ASB sticker bought tickets.

#100# people with an ASB sticker bought tickets.

Explanation:

We can set up a pair of simultaneous equations from the question:

Let #x =# the number of people with an ASB sticker that bought a ticket.

Let #y =# the number of people without an ASB sticker that bought a ticket.

1) #" "x + y = 160 " "#(the number of tickets sold)
2) #" "10x + 12y = 1720 " "#(the amount of money raised)

We can multiply the first equation by #10#:

3) #" "10x + 10y = 1600#

Then, subtract equation (3) from the equation (2):

#2y = 120#

Therefore, #y = 60#, so #60# people without an ASB sticker bought tickets.

Substitute #y = 60# into equation (1):

#x + y = 160#

#x + 60 = 160#

#x = 100#

so #100# people with an ASB sticker bought tickets.

Then, check your answer (optional):

#100 + 60 = "160 tickets sold"#

#(100 * $10) + (60 * $12) = $1000 + $720 = "$1720 raised"#