Question

The school that Chelsea goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 3 adult tickets and 13 student tickets for a total of $82. The school took in $142 on the second day by selling 13 adult tickets and 3 student tickets. find the price of an adult ticket and the price of a student ticket?

Answer 1

$\: \: \: \: \: \: \: \: \: \:\huge{\underline{\sf{\red{Solution}}}}$

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• Let the price of adult ticket be x.
• Let the price of student ticket be y.

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On the first day

→ Equation = 3x + 13y = 82⠀⠀...[1]

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On the second day

→ Equation = 13x + 3y = 142⠀⠀...[2]

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$\: \: \: \: \: \: \: \: \tiny\dag{\underline{\bf\: \: \: {Solving\: [1]\: and\: [2] }}}$

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We get :-

• x = 10
• y = 4

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Note (✓) :- Explanation is in attachment.

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Hence,

• Price of a adult ticket is Rs.10
• Price of a student ticket is Rs.4

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Answer 2

• Let ticket for Adult be x
• Let ticket for Students be y

$\sf3x + 13y = 82 \: \: \: \: \: \: (1)$

$\sf 13x + 3y = 142 \: \: \: \: (2)$

$\sf 39x + 169y = 1066 \: \: \: \: \: \: \: \: \: (3)$

$\sf 39x + 9y =426 \: \: \: \: \: \: \: \: \: \: (4)$

$\large \sf \cancel39x + 169y = 1066\\ \underline{ \large \sf \cancel39x + 9y \: \: \: = 426 } \\ \large \sf160y = 640 \implies y = \frac{640}{160}$

$\large \ \sf ⟹Ticket \: \: for \: \: Student \: ( y ) = 4$

$\sf 3x + 13(4) = 82$

$\sf 3x = 82 - 52 \: \: \implies x = \frac{30}{3}$

$\sf ⟹ Ticket \: \: for \: \: Adult \: (x )= 10$