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 $\$5$
• B. Cost of a child ticket is $\$3$
• C. Cost of an adult ticket is $\$8$
• D. Cost of a child ticket is $\$5$

Answer 1

Answer: (B), (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 $\$30$
$\Rightarrow 3x+2y=30$ $.......\left(1\right)$
Also, $2$ adults and $3$ children tickets cost $25\$$
$\Rightarrow 2x+3y=25$ $.......\left(2\right)$
Now, multiplying $2$ in equation $\left(1\right)$ and $3$ in equation $\left(2\right)$ we get,
$\Rightarrow 2(3x+2y)=30\times 2$ [from (1)]
$\Rightarrow 6x+4y=60$
$\Rightarrow 6x=60-4y$ $......\left(3\right)$
And,
$\Rightarrow 3(2x+3y)=25\times 3$
$\Rightarrow 6x+9y=75$
Substituting value of $6x$ from equation $\left(3\right)$ we get,
$\Rightarrow 60-4y+9y=75$
$\Rightarrow 5y=75-60$
$\Rightarrow y=3$

Substituting value of $y=3$ in equation $\left(3\right)$, we get:
$\Rightarrow 6x=60-4\times 3\Rightarrow 6x=48\Rightarrow x=8$

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