Question 122553
<pre>
<h3 style="font: bold times">
Solution
</h3>
<p style="font: courier">
Part a.
{{{g/b=19/17}}}

Cross-multiply
{{{17g=19b}}}

Divide by 17
{{{g=19b/17}}}

Part b.
We are given that the total number of students is 1908, and given the
presumption that all students have to be either boys or girls we can say:
{{{g+b=1908}}}

From part a. we have {{{17g=19b}}} which can be written:
{{{17g-19b=0}}}

Giving us a system of equations:
Eq. 1) {{{g+b=1908}}}
Eq. 2) {{{17g-19b=0}}}

Solve
Step 1: Multiply equation 1 by 19 resulting in equation 3
Eq. 3) {{{19g+19b=36252}}}

Add equation 2 to equation 3, term by term, resulting in equation 4
Eq. 3) {{{19g+19b=36252}}}
Eq. 2) {{{17g-19b=0}}}

Eq. 4) {{{cartoon(red(36g),36g+red(0b),36g+0b=red(36252))}}}

Divide equation 4 by 36:
{{{g=1007}}}

Knowing that there are 1007 girls, we can calculate the number of boys by:
{{{b=1908-g=1908-1007=901}}}

</p>
<hr/>
<h3 style="font: bold times">
Check Answer
</h3>
<p style="font: courier">
{{{901+1007=1908}}}
{{{17*1007=17119}}}
{{{19*901=17119}}}
</p>
</pre>