Q: An event has 18 more boys than girls. The total number of participants is 1000. How many boys & girls competed?

A:  Let B represent the number of “boys” and let G represent the number of “girls”.

We know that there are 18 more boys than girls, so:

(1) G + 18 = B.

We also know that there are a total of 1000 people, so:

(2) G + B = 1000.

Now, from equation (1) we have that B = G + 18 and we can substitue that into equation (2) like so:

G + B = 1000 and plug in (G + 18) for B to get:

G + (G+ 18) = 1000

And solve:

G + (G+ 18) = 1000

2G + 18 = 1000

2G = 982

G = 491.

There are 491 girls.  Since there are 1000 total people, we know that 1000 – 491 = 509.  There must be 509 boys.