Question 110465
Let x=length of pole in feet


So we know that half ({{{1/2}}}) of (which means "multiply") the pole (x) is in the ground. So {{{(1/2)x}}} would be the expression for the length of the pole in the ground.


We also know that a third {{{1/3}}} of the pole is underwater. So {{{(1/3)x}}} would be the expression for the length of the pole underwater.


Finally we know that 10 ft is above water. Now simply add all of the pieces of the pole to get the total length x


{{{(1/2)x+(1/3)x+10=x}}} this says that the sum of the parts equals the entire length of the pole



{{{6((1/2)x+(1/3)x+10)=6x}}} Multiply both sides by the LCD 6 to remove the fractions



{{{3x+2x+60=6x}}} Distribute and multiply 




{{{5x+60=6x}}} Combine like terms



{{{cross(5x-5x)+60=6x-5x}}} Subtract 5x from both sides



{{{60=x}}} Combine like terms



So the length of the pole is 60 ft



Notice if we take half of 60, we get 30; if we take a third of 60, we get 20. Now add 30, 20 and 10 to get



{{{30+20+10=60}}} So this verifies our answer.