Answer:
325 adult tickets were sold
Explanation:
- We will need a system of equations to determine the number of adult tickets that were told.
- In the system, we can let A represent the number of adult tickets sold and we can let S represent the number of student tickets sold.
First equation:
- The sum of the quantities of adult tickets and student tickets sold equals the total number of tickets sold.
Thus, the first equation in our system is given by:
A + S = 703
Second equation:
Since there 53 more student tickets sold than adult tickets, the second equation in our system is given by:
S = A + 53
Method to solve: Substitution:
- The second equation is already arranged in such a way that allows us to substitute it for S in the first equation to find A, the number of adult tickets sold:
Substituting S = A + 53 for S in A + S = 703:
A + A + 53 = 703
(2A + 53 = 703) - 53
(2A = 650) / 2
A = 325
Thus, 325 adult tickets were sold.
Optional Step: Check the validity of the answer:
- To check whether we've found the correct number of adult tickets sold, we'll first need to find the number of student tickets sold.
- We can do this by plugging in 325 for A in S = A + 53
Plugging in 325 for A in S = A + 53:
S = 325 + 53
S = 378
Thus, 378 student tickets were told.
- Since the sum of 325 and 378 is 703, the first statement is satisfied.
- Since 378 is 53 more than 325, the second statement is satisfied.
Therefore, we've correctly determine the number of adult tickets sold.