Question

Mark’s school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 4 senior tickets and 4 child tickets for a to total of 68. The school took in 120 on the second day by selling 12 senior tickets and 5 child tickets. Find the price of a senior ticket and a child ticket

Answer 1

The price of one adult ticket is 5 and price of one child ticket is 12.

Step-by-step explanation:

Let,

Price of one senior ticket = x

Price of one child ticket = y

According to given statement;

4x+4y=68         Eqn 1

12x+5y=120      Eqn 2

Multiplying Eqn 1 by 3

$3(4x+4y=68)\\12x+12y=204\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(12x+12y)-(12x+5y)=204-120\\12x+12y-12x-5y=84\\7y=84$

Dividing both sides by 7

$\frac{7y}{7}=\frac{84}{7}\\y=12$

Putting y=12 in Eqn 1

$4x+4(12)=68\\4x+48=68\\4x=68-48\\4x=20$

Dividing both sides by 4

$\frac{4x}{4}=\frac{20}{4}\\x=5$

The price of one adult ticket is 5 and price of one child ticket is 12.

Keywords: linear equation, elimination method

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