David had been pricing bus fares for a group trip to new york. three adults and four children must pay $159. two adults and three children must pay $112. find the price of an adult’s ticket and the price of a children’s ticket.

adult ticket cost $51.5

Children's ticket cost $1.125

Step-by-step explanation:

Let x represent the cost of one adult ticket.

Let y represent the cost of one children's ticket.

Three adults and four children must pay $159. This means that

3x + 4y = 159 - - - - - - -1

Two adults and three children must pay $112. This means that

2x + 3y = 112 - - - - - - - 2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 8y = 318 - - - - - - - -3

6x + 24y = 336 - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

-16y = -18

y = -18/-16 = 1.125

Substituting y = 1.125 into equation 1, it becomes

3x + 4×1.125 = 159

3x + 4.5 = 159

3x = 159 - 4.5 = 154.5

x = 154.5/3 = 51.5

ab will be equal to