Rollie was succesful in losing weight he had a goal weight in mind he went on a diet for three months each month he would lose o
ne third of the difference between his current weight and his goal weight and an additional three pounds at the end of three months he was just 3 pounds over his goal weight how many pounds did he lose in those three months? Explain
Let's say that in the beginning he weighted x and at the end he weighted x-y, y being the number of kg he wanted to loose.
first month he lost y/3
then he lost: (y-y/3)/3 this is (2/3y)/3=2/9y explanation: ((y-y/3) is what he still needed to loose: y minus what he lost already
and then he lost (y-2/9y-1/3y)/3+3 (the +3 is his additional 3 pounts) (y-2/9y-1/3y)/3-3=(7/9y-3/9y)/3+3=4/27y+3
it's not just y/3 because each month he lost one third of what the needed to loose at the current time, not in totatl
and the weight at the end of the 3 months was still x-y+3, 3 pounds over his goal weight!
so: x -y/3-2/9y-4/27y-3=x-y+3
we can subtract x from both sides: -y/3-2/9y-4/27y-3=-y+3 add everything up:
-19/27y=-y+6
which means -19/27y=-y+6
y-6=19/27y
8/27y=6 4/27y=3 y=20.25
so... that's how much he wanted to loose, but he lost 3 less than that, so 23.25
ps. i hope I didn't make a mistake in counting, let me know if i did. In any case you know HOW to solve it now, try to do the calculations yourself to see if they're correct!
