<u>Answer:</u>
Price of the adult's ticket = $13
Price of a child's ticket = $ 10
<u>Step-by-step explanation:</u>
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 =
x= 13
