High School

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Jessica's school is selling tickets to the annual talent show.

On the first day of ticket sales, the school sold 5 senior citizen tickets and 13 child tickets for a total of $146. On the second day, the school took in $219 by selling 11 senior citizen tickets and 14 child tickets.

What is the price of one senior citizen ticket and one child ticket?

Answer :

So, the price of one senior citizen ticket is approximately $11, and the price of one child ticket is approximately $7.

To solve this problem, let's denote:

x as the price of one senior citizen ticket

y as the price of one child ticket

Now, we can set up a system of equations based on the given information:

From the first day:

5x+13y=146 (total sales on the first day)

From the second day:

11x+14y=219 (total sales on the second day)

Now, we can solve this system of equations using substitution or elimination method. Let's use the elimination method:

Multiply the first equation by 14 and the second equation by 13 to eliminate

70x+182y=2044

143x+182y=2847

Now, subtract the first equation from the second equation:

143x+182y−(70x+182y)=2847−2044

Simplify:

73x=803

Now, divide both sides by 73:

[tex]$x=\frac{803}{73}$[/tex]

Now, let's calculate the value of

x≈11

Now that we have the value of x, we can substitute it into one of the original equations to find y. Let's use the first equation:

[tex]$\begin{aligned} & 5 x+13 y=146 \\ & 5(11)+13 y=146 \\ & 55+13 y=146 \\ & 13 y=146-55 \\ & 13 y=91 \\ & y=\frac{91}{13}\end{aligned}$[/tex]

Now, let's calculate the value of y≈7

So, the price of one senior citizen ticket is approximately $11, and the price of one child ticket is approximately $7.

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