*Don intended to place a mark 2 1/4 inches from one end of a narrow road 9 1/4 inches long, but he mistakenly placed the mark 2 1/4 inches from the other end of the road. How far, in inches, is his mark from the location where he intended to place it?
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How to do this problem?
Draw a picture and see if that helps. Mark the lengths of each piece of info you are given.
I did, and I got it wrong. It is saying “from one end” so should I mark on the rod or outside of the rod?
Ah, “rod.” I kept thinking a 9 1/4" road was pretty short.
Don’t change your frame of reference, I think… Keep everything in context of the same end of the road, err. rod.
He meant to place it 2 1/4 " from the (for example) “south” end.
He placed it 2 1/4" from the “north” end. How far is that from the “south” end?
So it’d be 2.25 + 9.25 + 2.25?
y…a…b…x
He wanted to put it at a. He put it at b.
a is a distance from y, b is a distance from y. x is a distance from y. the ONLY reason you need to know that the rod is 9 1/4 inches long is so you know that x is 9 1/4 inches from y, and that b is some number less than that away from y. Once you figure out how far b is from y, you can throw away the 9 1/4 (purge it from your mind).
to know the distance from a to b,
- understand that the distance from a to y (a-y = 2 1/4)
- discover the distance from b to y.
2.1) b to y is less than x to y.
2.2) x to y is 9.25.
2.3) x to b is 2.25.
2.4) so b to y would about have to be 2.25 less than the distance from x to y. - a to y has to be less than b to y. That’s because it’s a line, and a is between b and y, so it cannot be more.
- I really can’t go much further without actually typing the equation.
For it to be 2.25 + 9.25 + 2.25, he’d have to be putting the things 2 and a quarter inches beyond the ends of the rod. This is mathematically possible, but fantastically unstable 
so we should rule that out.
[edit: replaced dashes on first line with .'s since the dashes formatted oddly]
Is the answer 7?
@PP93291 No. Draw it out and label points for where Don placed and should’ve placed the mark.
The marks go on the rod.
Is the answer 4 3/4 ???