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Ralph spent $132 to buy movie tickets for 20 students and 4 adult chaperones. Adult tickets cost $3 more than student tickets. If A𝐴 is the price of an adult ticket and S𝑆 is the price of a student ticket, which system of equations could be used to find the price of each adult and student ticket? {A+S=320A+4S=132{𝐴+𝑆=320𝐴+4𝑆=132 {A=S+3A+S=132{𝐴=𝑆+3𝐴+𝑆=132 {S=A+34A+20S=132{𝑆=𝐴+34𝐴+20𝑆=132 {A=S+34A+20S=132{𝐴=𝑆+34𝐴+20𝑆=132

Question

Ralph spent 132tobuymovieticketsfor20studentsand4adultchaperones.Adultticketscost132 to buy movie tickets for 20 students and 4 adult chaperones. Adult tickets cost 3 more than student tickets. If A𝐴 is the price of an adult ticket and S𝑆 is the price of a student ticket, which system of equations could be used to find the price of each adult and student ticket? {A+S=320A+4S=132{𝐴+𝑆=320𝐴+4𝑆=132 {A=S+3A+S=132{𝐴=𝑆+3𝐴+𝑆=132 {S=A+34A+20S=132{𝑆=𝐴+34𝐴+20𝑆=132 {A=S+34A+20S=132{𝐴=𝑆+34𝐴+20𝑆=132

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Solution

The correct system of equations to solve this problem is:

{A=S+3 4A+20S=132

Here's why:

  1. We know that adult tickets cost $3 more than student tickets. This can be represented as A=S+3.

  2. We also know that Ralph spent $132 on 20 student tickets and 4 adult tickets. This can be represented as 4A+20S=132.

So, these two equations together form the system of equations that can be used to find the price of each adult and student ticket.

This problem has been solved

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