Question

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.

Answer 1

Price of the​ adult's ticket = $13

Price of a​ child's ticket = $ 10

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

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

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 =
`(39)/(3)`

x= 13