question about linear equations using substitution or elimination

Question

in part of a fundraising campaign, logan organized a dog show. The cost to rent the park was $1300 plus $2.50 per person for the snack bar fee. logan charged $5 for each student ticket and $8 for each adult ticket. his total sales were 3585 and the total attendance was 525 people. How many students attended the dog show? How many adults attended the dog show? How much money did logan raise with this event?

Answer 1

a = number of adults

s = number is students

 8a + 5s = 3585

a + s = 525

a = 525 - s

 

Using substitution

8(525 - s) + 5s = 3585

4200 - 8s + 5s = 3585

-3s = 3585 - 4200 = -615

s = 105

 

a +(105) = 525

a = 420

 

Costs

$1300 + $2.50(525)

= $1300 + $1312.50

= $2612.50

 

profit

$3585 - $2612.50 = $972.50