Ann Marie Jones is pricing train fares. Three adults and four children must pay $101. Two adults and three children must pay $72. We need to find the price of an adult's ticket and the price of a child's ticket. It says that the price of a child's ticket is $14, and we need to find the price of an adult's ticket.

1. Problem Description

Ann Marie Jones is pricing train fares. Three adults and four children must pay $

1

0

1. Two adults and three children must pay $

7

2. We need to find the price of an adult's ticket and the price of a child's ticket. It says that the price of a child's ticket is $14, and we need to find the price of an adult's ticket.

2. Solution Steps

Let $a$ be the price of an adult's ticket and $c$ be the price of a child's ticket.

We are given the following information:

$3a + 4c = 101$

$2a + 3c = 72$

We are also given that $c = 14$. We need to solve for $a$.

Substitute $c = 14$ into the two equations:

$3a + 4(14) = 101$

$2a + 3(14) = 72$

$3a + 56 = 101$

$2a + 42 = 72$

From the first equation:

$3a = 101 - 56$

$3a = 45$

$a = 45/3$

$a = 15$

From the second equation:

$2a = 72 - 42$

$2a = 30$

$a = 30/2$

$a = 15$

Both equations give the same value for $a$.

3. Final Answer

The price of an adult's ticket is $15.