Question

ann marie jones has been pricing train fares for a group trip to new york. three adults and four children must pay $129. two adults and three children must pay $92. find the price of the adult’s ticket and the price of a child’s ticket.
the price of a child’s ticket is $ 18
the price of an adult’s ticket is $\square

Explanation:

Step1: Define Variables

Let \( a \) be the price of an adult's ticket and \( c \) be the price of a child's ticket. We know \( c = 18 \) from the problem.

Step2: Use the First Equation

From "Three adults and four children pay $129", we have the equation \( 3a + 4c = 129 \).

Step3: Substitute \( c \) Value

Substitute \( c = 18 \) into the equation: \( 3a + 4(18) = 129 \).

Step4: Simplify and Solve for \( a \)

First, calculate \( 4(18) = 72 \). Then the equation becomes \( 3a + 72 = 129 \). Subtract 72 from both sides: \( 3a = 129 - 72 = 57 \). Divide both sides by 3: \( a = \frac{57}{3} = 19 \).

Answer:

The price of an adult’s ticket is $19.