Jen butler has been pricing speed pass train fares for a group trip to New York. Three adults and four children must pay $97. two adults and three children must pay $69. find the price of the adults ticket and the price of the child’s ticket.

The adult's ticket cost $15 and the child's ticket cost $13

Step-by-step explanation:

System of Equations

Let's call:

x = price of the adult's ticket

y = price of the child's ticket

Three adults and four children must pay $97, thus:

3x + 4y = 97       [1]

Two adults and three children must pay $69, thus:

2x + 3y = 69      [2]

Multiplying [1] by -2 and [2] by 3:

-6x - 8y = -194       [3]

6x + 9y = 207         [4]

Adding [3] and [4] (the x's cancel out):

-8y + 9y = 13

y = 13

From [1]

3x + 4*13 = 97

3x + 52 = 97

Subtracting 52:

3x = 45

Dividing by 3:

x = 15

The adult's ticket cost $15 and the child's ticket cost $13

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