Hi, I'm having some problems with word problems (again). The first one:
1) Imogene wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11-in by 14-in piece of cardboard as shown in the diagram. She figures that for versatility the area of the bottom must be 80in squared. What size square should she cut from each corner?
I realize this is a pretty common question, with a twist, but I can't get it to work out. Here's what I've got so far:
\(\displaystyle x(14 - 2x)(11 - 2x) = 0\)
\(\displaystyle 4x^3 - 50x^2 - 154x = 0\)
\(\displaystyle 4x^2 - 50x - 154 = 0\)
x should equal 1.72 but I can't see how. I know the 80 is supposed to go in there somewhere, but I don't know where.
The second one is this:
2) A small pipe is placed against a wall, but no block is used to keep it in place. There is a point on the edge of this pipe that is both 5in and 10in from the wall. Find two possibilities for the radius of the pipe.
I have no idea where to even start with this one. Any help would be appreciated, thanks.
1) Imogene wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11-in by 14-in piece of cardboard as shown in the diagram. She figures that for versatility the area of the bottom must be 80in squared. What size square should she cut from each corner?
I realize this is a pretty common question, with a twist, but I can't get it to work out. Here's what I've got so far:
\(\displaystyle x(14 - 2x)(11 - 2x) = 0\)
\(\displaystyle 4x^3 - 50x^2 - 154x = 0\)
\(\displaystyle 4x^2 - 50x - 154 = 0\)
x should equal 1.72 but I can't see how. I know the 80 is supposed to go in there somewhere, but I don't know where.
The second one is this:
2) A small pipe is placed against a wall, but no block is used to keep it in place. There is a point on the edge of this pipe that is both 5in and 10in from the wall. Find two possibilities for the radius of the pipe.
I have no idea where to even start with this one. Any help would be appreciated, thanks.