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Question

A family is travelling in metro. 3 adults and 2 children tickets cost $30, 2 adults and 3 children tickets cost $25. Find the costs of each adult and childrens ticket by substitution method.

A
Cost of an adult ticket is $5
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B
Cost of a child ticket is $3
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C
Cost of an adult ticket is $8
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D
Cost of a child ticket is $5
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Solution

The correct option is C Cost of an adult ticket is $8
Let the cost of the ticket for single adult be $x
And, cost of the ticket for a child be $y.
According to the question,
3 adults and 2 children tickets cost $30
3x+2y=30 .......(1)
Also, 2 adults and 3 children tickets cost 25$
2x+3y=25 .......(2)
Now, multiplying 2 in equation (1) and 3 in equation (2) we get,
2(3x+2y)=30×2 [from (1)]
6x+4y=60
6x=604y ......(3)
And,
3(2x+3y)=25×3
6x+9y=75
Substituting value of 6x from equation (3) we get,
604y+9y=75
5y=7560
y=3

Substituting value of y=3 in equation (3), we get:
6x=604×36x=48x=8

Cost of ticket for an adult is $8
Cost of ticket for a child is $3

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