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Zorluk: OrtaTranslating and Solving Algebraic Word Problems

A community theater group sells tickets for a play. Student tickets cost 1212 each, and adult tickets cost 1818 each. For a Friday night performance, the theater sold a total of 150150 tickets. The revenue from the adult tickets sold was 360360 more than the revenue from the student tickets sold. What is the absolute difference between the number of student tickets and the number of adult tickets sold for this performance?

  1. A
    78
  2. B
    72
  3. C
    54
  4. D
    30
  5. 6Cevap

Cevap

6
The correct answer is 6. By setting the number of student tickets to ss, the number of adult tickets is 150−s150 - s. Setting up the revenue relationship gives 18(150−s)=12s+36018(150 - s) = 12s + 360. Solving this equation gives s=78s = 78 student tickets and 150−78=72150 - 78 = 72 adult tickets. The absolute difference between the two values is 78−72=678 - 72 = 6.

Adım Adım Çözüm

1
Define variables for the unknown quantities.
Let ss be the number of student tickets sold. Since the total number of tickets sold was 150150, the number of adult tickets sold is 150−s150 - s.
Establishing single-variable representations allows us to model the entire situation using one equation.
2
Write an equation representing the revenue relationship.
The revenue from student tickets is 12s12s and the revenue from adult tickets is 18(150−s)18(150 - s). The equation is: 18(150−s)=12s+36018(150 - s) = 12s + 360.
The problem states that the adult ticket revenue was 360360 more than the student ticket revenue.
3
Solve the linear equation for ss.
2700−18s=12s+360  ⟹  2340=30s  ⟹  s=782700 - 18s = 12s + 360 \implies 2340 = 30s \implies s = 78.
Solving the equation gives the exact number of student tickets sold.
4
Calculate the number of adult tickets sold.
Adult tickets sold = 150−78=72150 - 78 = 72.
Subtracting the number of student tickets from the total ticket count yields the number of adult tickets.
5
Find the absolute difference between the two quantities.
∣78−72∣=6|78 - 72| = 6.
The question asks for the absolute difference between the number of student tickets and the number of adult tickets sold.

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Translating and Solving Algebraic Word Problems
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