Question 98811
First set some variables
Let's say boys = b and girls = g
Given that there are 17 more girls than boys we can show that as:
{{{g = b + 17}}}
We are also given the total number of all students is 431 and so:
{{{b + g = 431}}}
Now since we have established that {{{g = b + 17}}} we can subsitute b + 17 for 
the g in {{{b + g = 431}}} which gives us this:
{{{b + (b + 17) = 431}}}
We now have an equation with only one variable to solve for
so lets solve for b:
b + b + 17 = 431
2b + 17 = 431
2b = 414
b = 207
Now that we have solved for b we can use that value to solve for g in
{{{g = b + 17}}}
g = 207 + 17
g = 224
Finally we can check our answers by pluging them into {{{b + g = 431}}}