An athletic department sold 454 tickets to a sporting event. adults paid $3.50 per ticket, and students paid $1.00. the total ticket sales were $1,154. if 20 more adult tickets and 20 fewer student tickets had been sold, which statements would be correct? mark all that apply.

Let a and s be the number of adults and students respectiviely:

a+s=454

a=454-s  and we are also told:

3.5a+s=1154, using a found above in this equation yields:

3.5(454-s)+s=1154 perform indicated multiplication on left side

1589-3.5s+s=1154 combine like terms on left side

1589-2.5s=1154  subtract 1589 from both sides

-2.5s=-435

s=174, since a=454-s

a=280

So 280 adult and 174 student tickets were sold.

If 20 more adult and 20 less student tickets were sold they would have had ticket sales of:

3.5(280+20)+(174-20)=$1204

Wow. that is a really cool question.