Nathaniel school is selling tickets to a spring Musical on the first day of ticket sales the school so 3 senior citizen tickets and nine children tickets to for a total of $75 the school took in $67 on the school on the second day by 8 senior tickets and 5 child tickets. What is the prise each of one senior citizens ticket and one child ticket
To solve this problem, let's assign variables to the unknowns. Let's say the price of a senior citizen ticket is "S" and the price of a child ticket is "C".
From the given information, we can create two equations:
Equation 1: 3S + 9C = 75 (from the first day of ticket sales)
Equation 2: 8S + 5C = 67 (from the second day of ticket sales)
To find the price of one senior ticket and one child ticket, we need to solve this system of equations.
Method 1: Substitution Method
Step 1: Solve Equation 1 for S:
3S + 9C = 75
3S = 75 - 9C
S = (75 - 9C)/3
S = 25 - 3C
Step 2: Substitute this expression for S into Equation 2:
8S + 5C = 67
8(25 - 3C) + 5C = 67
200 - 24C + 5C = 67
-19C = -133
C = (-133)/(-19)
C = 7
Step 3: Substitute the value of C back into Equation 1 to find S:
3S + 9C = 75
3S + 9(7) = 75
3S + 63 = 75
3S = 75 - 63
3S = 12
S = 12/3
S = 4
Therefore, the price of one senior citizen ticket is $4, and the price of one child ticket is $7.
Method 2: Elimination Method
Step 1: Multiply Equation 1 by 8 and Equation 2 by 3 to eliminate the S term:
24S + 72C = 600 (Equation 1)
24S + 15C = 201 (Equation 2)
Step 2: Subtract Equation 2 from Equation 1 to eliminate S:
(24S + 72C) - (24S + 15C) = 600 - 201
57C = 399
C = 399/57
C = 7
Step 3: Substitute the value of C back into Equation 1 to find S:
3S + 9C = 75
3S + 9(7) = 75
3S + 63 = 75
3S = 75 - 63
3S = 12
S = 12/3
S = 4
Again, we find that the price of one senior citizen ticket is $4, and the price of one child ticket is $7.
So, the price of one senior citizen ticket is $4, and the price of one child ticket is $7.
3s + 9c = 75 **
8s + 5c = 67 ***
** times 5 ---> 15s + 45c = 375
*** times 9 --> 72s + 45c = 603
subtract them:
57s = 228
s = $4.00
sub s = 4 into ** and solve for c