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admissions to a baseball game is 4 dollars for general admission and 5.50 dollars for reserve seats the receipts were 5,196.50 for 1,181 paid admissions how much of each ticket was sold?​

 Mar 21, 2021
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Hey there!

 

Here we want to create 2 equations so we can solve for each variable. We want to let \(g\)=general admission and \(r\)=reserve seats. We also know that there were 1181 tickets/seats bought and im assuming for a total cost of $5196.50. From this, we can gather that:

 

\(g+r=1181\)

\(4g+5.5r=5196.5\)

 

From this I will use elimination to remove a variable. I will multiply equation 1 by 4 and take it away from equation 2:

 

\(4g+4r=4724\) (eq 1 * 4, now take this from equation 2)

\(0g+1.5r=472.5\) (now rearrange to find \(r\))

\(r=315\)

 

Now that we know this, we can sub it back into the first equation to find \(g\)

 

\(g=866\)

 

Just to double check you can sub both into either equation to ensure it works:

 

\(5196.5=4(866)+5.5(315)\)

 

Hope this helped :) let me know how you go!

 Mar 22, 2021

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