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35 votes
35 votes
The school that Trevon goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 12 adult tickets and 2 student tickets for a total of $134. The school took in $186 on the second day by selling 13 adult tickets and 8 student tickets. What is the price each of one adult ticket and one student ticket?

User Firmino Changani
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1 Answer

22 votes
22 votes

Let the number of adult tickets sold be represented by a

Let the number o student tickets sold be represented by s

On the first day

12 adult tickets were sold and 2 students tickets were sold

=> 12a + 2s

The amount equals $134

12a + 2s = 134 ........ Equation 1

On the second day

13 adult tickets were sold and 8 students tickets which equal $ 186

13a + 8s = 186 ------ Equation 2

Equations 1 and 2 can be solved simultaneously

Using the Elimination Method

Equation 1 can be multiplied by 4 so that the variable s will be eliminated

=> 48a + 8s = 536 ---- Equation 3

Equation 2 can now be subtracted from equation 3

48a - 13a = 536 - 186

35a = 350

Divide both sides by 35

a =350/ 35

a = 10

To get s, substitute a = 10 into Equation 1

12a + 2s = 134

12 x 10 + 2s = 134

120 + 2s = 134

2s = 134 - 120

2s = 14

Divide both sides by 2

s = 7

The price of an adult ticket is $10

The price of a student ticket is $7

User Zapcost
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