Question

PLEASE HELP ME
WILL GIVE BRAINLIEST
PLEASE 20 POINTS
a stadium has 55,000 seats. seats sell for $25 in section A, $20 in section B, and $15 in section C. the number of seats in section A equals the total number of seats in sections B and C. suppose the stadium takes in $1,174,000 from each sold-out event. how many seats does each section hold?

Answer 1

Answer:

Section A has 27,500 seats.

Section B has 14,800 seats.

And Section C has 12700 seats.

Step-by-step explanation:

Let A represent the number of seats in Section A, B in Section B, and C in Section C.

We know that the stadium has a total of 55,000 seats. In other words:

$A+B+C=55000$

We also know that the stadium took in a total of $1,174,000. Remember that a seat in A is $25, B is $20, and C is $15. So:

$25A+20B+15C=1174000$

Also, we know that the number of seats in A is equivalent to the combined seats in B and C. So:

$A=B+C$

This is a system of equations. We can solve this by substitution.

First, let's substitute our third equation into our second equation. This yields:

$25(B+C)+20B+15C=1174000$

Distribute:

$25B+25C+20B+15C=1174000$

Combine like terms:

$45B+40C=1174000$

Let's divide everything by 5:

$9B+8C=234800$

Now, let's solve for either B or C. To do so, let's substitute our third equation into our first equation. This yields:

$(B+C)+B+C=55000$

Combine like terms:

$2B+2C=55000$

Divide everything by 2:

$B+C=27500$

I'm going to solve for B. Subtract C from both sides. This gives:

$B=27500-C$

Now, let's substitute this into the equation we acquired previously. This yields:

$9(27500-C)+8C=234800$

Distribute:

$247500-9C+8C=234800$

Subtract 247,500 from both sides:

$-9C+8C=-12700$

Add:

$-C=-12700$

Divide both sides by -1. So, the number of seats in Section C is:

$C=12700$

Now, we can solve for A and B.

Remember that there are 55,000 seats in total. So:

$A+B+C=55000$

We know that C is 12700. Substitute:

$A+B+12700=55000$

Subtract 12700 from both sides:

$A+B=42300$

Now, remember that A is B+C. So, substitute:

$B+C+B=42300$

Combine like terms. Again, let's substitute 12700 for C. This yields:

$2B+12700=42300$

Subtract 12700 from both sides:

$2B=29600$

Divide both sides by 2:

$B=14800$

Finally, to find A, we can use the first equation again:

$A+B+C=55000$

Substitute 14800 for B and 12700 for C. This gives us:

$A+14800+12700=55000$

Add:

$A+27500=55000$

Subtract 27500 from both sides. So:

$A=27500$

Therefore, there are 27,500 seats in Section A, 14,800 seats in Section B, and 12,700 seats in Section C.

And we're done!