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”.

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:

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:

.

Every clubhouse seat will add $12.00 to the receipt. clubhouse seats will add $ to the receipt. Similarly, grandstand seats will add $ to the receipt. The two values shall add up to $250,000.

Drop the dollar sign to get the second equation:

.

Hence the system:

.

Solve this system.

The first non-zero coefficient in equation is already one. That's the coefficient for . Use multiples of equation to get rid of in other equations (equation in this case.)

times equation is

.

Add to to get:

.

Divide both sides by -7 to get:

.

Add -1 times this equation to equation to get:

.

That is:

.

In other words,

366

step-by-step explanation: