Final answer:
The price of an adult ticket is $19, and the price of a child's ticket is $12. This was determined by creating a system of equations from the given scenarios and solving for the variables representing the ticket prices.
Step-by-step explanation:
Jen Butler is pricing Speed-Pass train fares for a group trip to New York. We have two different scenarios that we will use to set up a system of equations to figure out the individual prices of adult tickets and child tickets. Let's define A as the price of an adult ticket and C as the price of a child's ticket.
From the information given:
om the information given:
3 adults and 4 children must pay $105: 3A + 4C = 105
2 adults and 3 children must pay $74: 2A + 3C = 74
To solve this, we multiply the second equation by -1.5 to eliminate the adult ticket variable (A):
-1.5(2A + 3C = 74) gives us -3A - 4.5C = -111
Adding this to the first equation (3A + 4C = 105) gives us:
-0.5C = -6, or C = 12 after multiplying by -2.
Now we can substitute the value of C back into one of the original equations:
2A + 3(12) = 74
2A + 36 = 74,
so 2A = 38, and therefore, A = 19.
The price of an adult ticket is $19, and the price of a child's ticket is $12.