Question

Jen butler has been pricing speed pass train fares for a group trip to New York. Three adults and four children must pay $87. Two adults and three children must pay $62. Find the price of adults ticket and price of child's ticket.

Answer 1

The first thing we must do for this case is to define variables.
 We have then:
 x: price of adult's ticket
 y: price of child's ticket
 We now write the system of equations:
 $3x + 4y = 87 2x + 3y = 62$
 Solving the system of equations we have:
 x = 13 $
 y = 12 $
 Answer:
 the price of adults ticket and price of child's ticket are $ 13 and $ 12, respectively

Answer 2

Adults cost $13 and children cost $12.

To solve this, we will write and solve a pair of linear equation. A will represent the cost of an adult ticket and c will represent the cost of a children's ticket.

We have:

3a + 4c = 87
2a + 3c = 62

We can multiply the top equation by 2 and the bottom equation by -3.

We will have:

6a + 8c = 174
-6a + -9c = 186

Adding them gives us:
-1c = -12
or just c = 12

Substitute in 12 for c and we will find that a = 13
3a + 48  = 87
3a = 39
a = 13