if total ticket sales were $1625 adult tickets were $7.00 and student tickets were $3.00 and twice as many students bought tickets than adults, how many students and adult tickets were sold?
7 a + 3 s = 1625
s = 2 a
so
7 a + 3 (2 a) = 1625
7 a + 6 a = 1625
13 a = 1625
a = 125
so s = 250
To solve this problem, let's define some variables:
Let A represent the number of adult tickets sold.
Let S represent the number of student tickets sold.
From the given information, we can set up two equations:
1. The total ticket sales equation: 7A + 3S = 1625 (since adult tickets cost $7 and student tickets cost $3)
2. The equation representing the fact that twice as many students bought tickets than adults: S = 2A (since the number of student tickets sold is twice the number of adult tickets sold)
Now we can use these equations to solve for the values of A and S.
First, substitute the value of S from equation 2 into equation 1:
7A + 3(2A) = 1625
7A + 6A = 1625
13A = 1625
A = 1625 / 13
A ≈ 125
So, the number of adult tickets sold is approximately 125.
Substitute this value of A into equation 2 to find the number of student tickets sold:
S = 2A
S = 2(125)
S = 250
Therefore, the number of student tickets sold is 250.
To summarize:
- The number of adult tickets sold is approximately 125.
- The number of student tickets sold is 250.