Question

1. at a school fundraiser, 5 student tickets and 8 adult tickets sold for $94. then 10 student tickets and 12 adult tickets sold for $152. if the school sold 75 student tickets and 100 adult tickets total, how much money was collected? show your work. work space:

Explanation:

Step1: Define variables

Let $s$ = student ticket price, $a$ = adult ticket price.

Step2: Set up equations

$5s + 8a = 94$ (Eq1), $10s + 12a = 152$ (Eq2)

Step3: Simplify Eq2

Divide Eq2 by 2: $5s + 6a = 76$ (Eq3)

Step4: Subtract Eq3 from Eq1

$(5s + 8a) - (5s + 6a) = 94 - 76$ → $2a = 18$ → $a = 9$

Step5: Find $s$ using Eq1

$5s + 8(9) = 94$ → $5s + 72 = 94$ → $5s = 22$ → $s = 4.4$

Step6: Calculate total money

$75s + 100a = 75(4.4) + 100(9) = 330 + 900 = 1230$

Wait, correction in Step5: $5s = 94 - 72 = 22$ → $s = 4.4$ is correct. Then 754.4=330, 1009=900, total 1230.

Final Answer: $1230

Step1: Define variables

Let $s$ = student ticket price, $a$ = adult ticket price.

Step2: Set up equations

$5s + 8a = 94$; $10s + 12a = 152$

Step3: Simplify second equation

$5s + 6a = 76$

Step4: Solve for $a$

Subtract simplified eq from first: $2a=18$ → $a=9$

Step5: Solve for $s$

$5s=94-72=22$ → $s=4.4$

Step6: Calculate total revenue

$75×4.4 + 100×9 = 330 + 900 = 1230$

Answer:

$1550