SOLUTION: The local theater group anticipates that it can sell about 450 adult tickets and 700 student tickets for an upcoming show. The price of adult tickets will be $3 more than the price

Question 1203891: The local theater group anticipates that it can sell about 450 adult tickets and 700 student tickets for an upcoming show. The price of adult tickets will be $3 more than the price of student tickets. How much should each ticket cost if they intend to take in $9,400 from ticket sales?
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer:
Students = $7
Adults = $10

Scratch work shown

x = price for students
x+3 = price for adults

700x = revenue from the students
450(x+3) = revenue from the adults
700x+450(x+3) = total revenue = 9400
700x+450(x+3) = 9400

Solving for x.
700x+450(x+3) = 9400
700x+450x+1350 = 9400
1150x+1350 = 9400
1150x = 9400-1350
1150x = 8050
x = 8050/1150
x = 7
x+3 = 7+3 = 10

The price for each student should be $7, while the price for each adult should be $10.

Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!

The 450 adult tickets, each costing $3 more than a student ticket, bring in an "additional" 450($3) = $1350.

So the total of $9400 can be thought of as 450+700 = 1150 tickets costing the same amount, plus the additional $1350. That means the 1150 tickets that each cost the same sell for a total of $9400-$1350 = $8050. The cost for each of them is then $8050/1150 = $7.

ANSWER: The student tickets should cost $7 each, the adult tickets $7+$3 = $10 each.

Solving the problem in exactly the same way using formal algebra looks like this:

x = cost of a student ticket
x+3 = cost of an adult ticket

700(x)+450(x+3) = 9400
700x+450x+1350 = 9400
1150x = 8050
x = 8050/1150 = 7

Student ticket cost: x = $7
Adult ticket cost: x+3 = $10

Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!

PRICE$ QUANTITY COSTS ADULT x+3 450 450(x+3) STUDENT x 700 700x TOTAL 9400

That and what should follow are self explanatory.
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