8,400 were sold $6.00 for adult $4.00 for child ticket sales totaled $40,000 how many adult and child tickets were sold

Let x be the number of adult tickets sold and let y be the number of children's tickets sold.

So     x + y  = 8400

And the number of adult tickets sold times the price for each plus the number of children's tickests sold times their price = $40,000   or, in equation form

6x + 4y = 40000         Now, if we subtract x from both sides of the first equation, we have that y = 8400 - x

And substituting for y in the second equation, we have

6x + 4(8400 - x) = 40000    .....simplifying, we have

6x + 33600 - 4x = 40000

2x + 33600 = 40000    ..... subtract 33600 from both sides

2x = 6400     ...... divide by 2 on both sides

x = 3200    .......so this is the number of adult tickets sold

And using y = 8400 - x,  we have y = 8400 - 3200 = 5200   ..and that's how many children's tickets were sold.