Mathematics, 25.06.2019 15:10 jwbri

1. there were 36,000 people at a horse race in lexington, kentucky. the day'sreceipts were $250,000. the only two types of seats available were clubhouseor grandstand seats. how many people paid $12.00 for clubhouse seats andhow many people paid $5.00 for grandstand seats? only an algebraic solutionwill earn credit. state what any variables represent by writing a "let statement”.

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Answer from: Ezasha

10000 people paid $12.00 each for clubhouse seats and26000 people paid $5.00 each for grandstand seats.

Step-by-step explanation:

The question is asking for a system of equations, which make explanations easy. :)

Define the variables. Setting to the number of clubhouse seats sold and to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:

Let

be the number of clubhouse seats sold.Let

be the number of grandstand seats sold.

The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.

Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:

x + y = 36000 .

Every clubhouse seat will add $12.00 to the receipt. clubhouse seats will add $ $12\;x$ to the receipt. Similarly, grandstand seats will add $ $5\;y$ to the receipt. The two values shall add up to $250,000.

Drop the dollar sign to get the second equation:

$12\;x +5\;y =250000$ .

Hence the system:

$\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}$ .

Solve this system.

The first non-zero coefficient in equation $\textcircled{\raisebox{-0.9pt}1}$ is already one. That's the coefficient for . Use multiples of equation $\textcircled{\raisebox{-0.9pt}1}$ to get rid of in other equations (equation $\textcircled{\raisebox{-0.9pt}2}$ in this case.)

times equation $\textcircled{\raisebox{-0.9pt}1}$ is

$-12 \;x - 12\;y = -432000$ .

Add $-12\times \textcircled{\raisebox{-0.9pt}1}$ to $\textcircled{\raisebox{-0.9pt}2}$ to get:

$0\;x + -7\;y = -182000$ .

Divide both sides by -7 to get:

y = 26000 .

Add -1 times this equation to equation $\textcircled{\raisebox{-0.9pt}1}$ to get:

x = 10000 .

That is:

$\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}$ .

In other words,

10000 clubhouse seats were sold, and26000 grandstand seats were sold.

Answer from: Quest

the answer is 45 i just did it on oddesy ware

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

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1. there were 36,000 people at a horse race in lexington, kentucky. the day'sreceipts were $250,000....

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