Question 186021
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*Remember:
{{{Jane=x}}} & {{{Beth=y}}}
1st condition:
{{{3x=8y}}}
2nd condition:
{{{x-y=15}}}---->{{{x=15+y}}}, EQN 1 & subst. in Condtn 1:
.
{{{3(15+y)=8y}}}
{{{45+3y=8y}}}
{{{8y-3y=45}}}---->{{{5y=45}}}--->{{{cross(5)y/cross(5)=cross(45)9/cross(5)}}}
{{{highlight(y=9yrs)}}}, Beth's Age 
Via EQN 1:
{{{x=15+9=highlight(24yrs)}}},  Jane's Age
Check via Condtn 2:
{{{3*24=8*9}}}
{{{72=72}}}
See graph for reference:
{{{drawing(400,400,-12,60,-12,60,grid(1),graph(400,400,-12,60,-12,60,x-15),green(locate(15,-2,Jane=24)),green(locate(.9,12,Beth=9)),blue(circle(24,0,.8)),blue(circle(0,9,.8)),circle(24,9,.65))}}}
Thank you,
Jojo</pre>