The problem states that Breana sold 3 senior citizen tickets and 1 child ticket on the first day, totaling $38. On the second day, she sold 3 senior citizen tickets and 2 child tickets, totaling $52.
To find the price of a senior citizen ticket, we can set up an equation using the given information. Let's denote the price of a senior citizen ticket as "s" and the price of a child ticket as "c".
On the first day, Breana sold 3 senior citizen tickets and 1 child ticket, which gives us the equation:
3s + 1c = 38
On the second day, she sold 3 senior citizen tickets and 2 child tickets, which gives us the equation:
3s + 2c = 52
We can now solve these equations simultaneously to find the values of "s" and "c".
From the first equation, we can isolate "c" by subtracting 3s from both sides:
1c = 38 - 3s
Substituting this value of "c" into the second equation, we get:
3s + 2(38 - 3s) = 52
Simplifying the equation:
3s + 76 - 6s = 52
Combining like terms:
-3s + 76 = 52
Subtracting 76 from both sides:
-3s = -24
Dividing both sides by -3:
s = 8
Therefore, the price of a senior citizen ticket is $8.
To find the price of a child ticket, we can substitute the value of "s" into one of the original equations. Let's use the first equation:
3(8) + 1c = 38
24 + 1c = 38
Subtracting 24 from both sides:
1c = 14
Therefore, the price of a child ticket is $14.
In conclusion, the price of a senior citizen ticket is $8 and the price of a child ticket is $14.