Question

At a regional soccer​ tournament, tickets for two adults and seven students cost ​$42. Tickets for three adults and eleven students cost ​$65. Determine the price of an adult ticket and the price of a student ticket.

Answer 1

The cost of adult ticket is $7 and child ticket is $4.

Step-by-step explanation:

Let,

Price of one adult ticket = x

Price of one child ticket = y

According to given statement;

2x+7y=42    Eqn 1

3x+11y=65   Eqn 2

Multiplying Eqn 1 by 3

$3(2x+7y=42)\\6x+21y=126\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 2

$2(3x+11y=65)\\6x+22y=130\ \ \ Eqn\ 4$

Subtracting Eqn 3 from Eqn 4

$(6x+22y)-(6x+21y)=130-126\\6x+22y-6x-21y=4\\y=4$

Putting y=4 in Eqn 1

$2x+7(4)=42\\2x+28=42\\2x=42-28\\2x=14$

Dividing both sides by 2

$\frac{2x}{2}=\frac{14}{2}\\x=7$

The cost of adult ticket is $7 and child ticket is $4.

Keywords: linear equation, elimination method

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