1000 people attended a concert - Junior Cycle Mathematics - Question 11 - 2014

This equation illustrates the total revenue from ticket sales, where each adult ticket is €10 and each child's ticket is €5.

Starting with the equations:

1. $x + y = 1000$
2. $10x + 5y = 8750$

First, rearranging the first equation for y gives:

$y = 1000 - x$

Substituting this value of y in the second equation:

$10x + 5(1000 - x) = 8750$

Expanding the equation leads to:

$10x + 5000 - 5x = 8750$

Combining like terms results in:

$5x + 5000 = 8750$

Subtracting 5000 from both sides:

$5x = 3750$

Dividing by 5 gives:

$x = 750$

Now substituting back to find y:

$y = 1000 - 750 = 250$

Thus, the number of adults is 750 and the number of children is 250.