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.

Question

Mathematics

Kash Crane

29 May, 20:23

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.

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Answers (1)

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Fluffy · Answer 1

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