Please help me with the following question

Question

A concert hall with 1000 seats is completely filled with x boys, y girls and adults. Admission fee for an adult is $10 while a child pays 1/2 the price. Find in terms of x and y, the total amount collected.

Answer 1

Does   y = girls and adults

or         y = girls 

and.     z = adults?

 

Answer 2

Let A = #adults and T = total amount collected.

 

We have x + y + A = 1000 (completely filled concert hall)

 

T = 10A + 5(x+y)   ($10 for adults, $5 for boys and girls).

 

If we solve the first equation for A, we get A = 1000 - (x+y)

 

Substitute that expression into the 2nd equation and simplify to get T in terms of x and y:

 

T = 10 [1000 -(x+y)] + 5(x+y)

 

T = 10000 - 5x - 5y (that's one way to write it)