Jen butler has been pricing speed-pass train fares for a group trip to new york. three adults and four children must pay $ 79. two adults and three children must pay $ 56. find the price of the adult's ticket and the price of a child's ticket.

Price of the adult's ticket = $13

Price of a child's ticket = $ 10

Step-by-step explanation:

Given:

Cost of train fares for Three adults and four children = $79

Cost of train fares Two adults and three children  = $ 56

To Find:

Price of the adult's ticket and the price of a child's ticket =?

Solution:

Let the cost of one adult's ticket be x  and

Let the cost of one child's ticket be y

Then

Three adults and four children must pay $ 79 be

3x + 4y = 79-----------------------------------------------(1)

Two adults and three children must pay $56

2x + 3y = 56----------------------------------------------(2)

multiply  eq(1) by 2, we get

6x + 8y = 158----------------------(3)

multiply  eq(2) by 3, we get

6x + 9y = 168----------------------(4)

Subracting (3) from (4)

 6x + 9y = 168

 6x + 8y = 158

(-)      (-)       (-)

------------------------------

0x +  y = 10

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y=10

Now substitute the value of y in eq (1) to get the value of x

3x + 4(10)= 79

3x +  40 = 79

3x = 79 - 40

3x = 39

x =

x= 13

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