Need help with the table for this problem. already solved for x and y just not sure how to place info on the table ( I solved using the elimination method )

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asked Sep 10, 2024 20.1k views

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Kartik Sharma · Answer 1 · 2024-09-17T02:45:57+0000

Answer:

At the carnival, 400 adult tickets were sold and 300 child tickets were sold.

Explanation:

Define Variables

Let x be the number of adult tickets
Let y be the number of child tickets

Create System

A total of 700 tickets were sold:

$\implies x+y=700$

Given an adult ticket cost $10 and a child's ticket cost $5, and the total amount of tickets sold is $5,500:

$\implies 10x+5y=5500$

Therefore, the system of equations that models the given problem is:

$\begin{cases}x+y=700\\10x+5y=5500\end{cases}$

Solve the System

Rearrange the first equation to isolate y:

$\implies y=700-x$

Substitute the found expression for y into the second equation to eliminate y:

$\implies 10x+5(700-x)=5500$

Solve the equation for x:

$\implies 10x+3500-5x=5500$

$\implies 5x+3500=5500$

$\implies 5x=2000$

$\implies x = 400$

Therefore, 400 adult tickets were sold.

Substitute the found value of x into the equation for y and solve for y:

$\implies y=700-400$

$\implies y=300$

Therefore, 300 child tickets were sold.

Check your Answer

Substitute the found values of x and y into the two equations:

$\begin{aligned}x+y&=700\\ \implies 400+300&=700\\700&=700 \leftarrow \sf correct\end{aligned}$

$\begin{aligned}10x+5y&=5500\\ \implies 10(400)+5(300)&=5500\\4000+1500&=5500\\5500&=5500 \leftarrow \sf correct\end{aligned}$