Question

A man buys 5 first class tickets and 2 second class tickets which cost him Rs. 246. Another
man buys 2 first class and 3 second class tickets which cost him Rs. 149.
Let the price of a first class ticket be Rs. x and the price of a second class ticket be Rs. y.
a) Write down a pair of simultaneous equations involving x and y.
b) Find x and y.

Answer 1

Let :

• Cost of first class ticket = Rs. x
• Cost of second class ticket = Rs. y

Given :

• Total cost of 5first class ticket & 2 second class ticket = Rs. 246
• Total cost of 2 first class ticket & 3 second class ticket = Rs. 149

To find :

• Equation for above condition
• Find x & y

Solution :

Total cost of 5first class ticket & 2 second class ticket = 5x + 2y

=> 5x + 2y = 246 ...........equation 1

=> 5x = 246 - 2y

=> x = (246 - 2y) ÷ 5 .........equation 2

Total cost of 2 first class ticket & 3 second class ticket = 2x + 3y

=> 2x + 3y = 149

putting value of x from equation 2, we get

$\sf \implies \: 2( \dfrac{(246 - 2y)}{5} ) + 3y = 149 \\ \\ \sf \implies \: \dfrac{(492 - 4y)}{5} + 3y = 149 \\ \\ \sf taking \: lcm \\ \sf \implies \: \dfrac{(492 - 4y) + (3y \times 5)}{5} = 149 \\ \\ \sf taking \: lcm \\ \sf \implies \: \dfrac{492 - 4y + 15y}{5} = 149 \\ \\ \sf \implies \: 492 + \: 11y = 149 \times 5 \\ \\ \sf \implies \: 11y = 745 \: - \: 492 \\ \\ \sf \implies \: 11y = 253 \\ \sf \implies \: y = \: \dfrac{253}{11} \\ \\ \sf \implies \: \bold{y = \: 23}$

Putting value of y in equation 2 , {x = (246-2y)÷5}

we get;

$\sf \implies \: x \: = \dfrac{246 - (2 \times 23)}{5} \\ \\ \sf \implies \: x \: = \dfrac{246 - 46}{5} \\ \\ \sf \implies \: x \: = \dfrac{200}{5} \\ \\ \sf \implies \: \bold {x \: = 40}$

ANSWER :

a) Equation

• 5x + 2y = 246
• 2x + 3y = 149

b) Value

• x = ₹40
• y = ₹23

Answer 2

Answer:

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Step-by-step explanation: