Mrs. Gilmore bought 26 student tickets and 29 adult tickets which cost a total of $959. Mr. thompson bought 28 student tickets and 29 adult tickets for a total cost of $977. what is the price for each student and adult ticket
Let's assume the price of a student ticket is S and the price of an adult ticket is A.
According to the problem, Mrs. Gilmore bought 26 student tickets, so the total cost of student tickets for her is 26S.
She also bought 29 adult tickets, so the total cost of adult tickets for her is 29A.
Therefore, the total cost for Mrs. Gilmore is 26S + 29A = $959. ----(equation 1)
Similarly, Mr. Thompson bought 28 student tickets, so the total cost of student tickets for him is 28S.
He also bought 29 adult tickets, so the total cost of adult tickets for him is 29A.
Therefore, the total cost for Mr. Thompson is 28S + 29A = $977. ----(equation 2)
To solve these equations, we need to eliminate one of the variables. Let's multiply equation 1 by 28 and equation 2 by 26:
28 * (26S + 29A) = 28 * $959
26 * (28S + 29A) = 26 * $977
Simplifying these equations gives us:
728S + 812A = $26852 ---(equation 3)
728S + 754A = $25302 ---(equation 4)
By subtracting equation 4 from equation 3, we can eliminate the variable S:
728S + 812A - (728S + 754A) = $26852 - $25302
812A - 754A = $1543
58A = $1543
Dividing both sides by 58 gives us:
A = $1543 / 58
A ≈ $26.67
Substituting the value of A into equation 3:
728S + 812($26.67) = $26852
728S + $21660.04 = $26852
728S = $26852 - $21660.04
728S = $5191.96
Dividing both sides by 728 gives us:
S = $5191.96 / 728
S ≈ $7.13
Therefore, the price for each student ticket is approximately $7.13, and the price for each adult ticket is approximately $26.67.