Chapter 21: Ten Classic Brainteasers
How Many Weights?
A merchant has a balance scale (refer to Figure 21-4) and wants to be able
to weigh any item between 1 and 50 pounds, to the nearest pound. How m
312
Part V: The Part of Tens
Figure 21-4:
A balance
scale is
level when
the items
weigh the
same.
Answer: Put three nuggets in one tray and three nuggets in the other tray.
If the scale is balanced, t
324
Math Word Problems For Dummies
area (continued)
hexagons, 271272
Norman windows, 279281
outside a perimeter, 273275
posters, 275279
problems, 31, 3334
rectangles
into circles, 281285
fencing, 2652
Chapter 20: Volumizing and Improving Your Surface
9 inches minus the two corners or 9 4 = 5 inches. The volume of the prism
is V = 8(5)(2) = 80 cubic inches.
In the calculus problem involving the open
Chapter 20: Volumizing and Improving Your Surface
Find the volume of a pile of sand thats 10 feet tall and compare it to the
volume of a pile of sand thats 12 feet all. The pile of sand thats 10 feet
Chapter 20: Volumizing and Improving Your Surface
If youre sending something that will fit into any size box and are restricted
only by the total volume, then you have more flexibility with the postal
308
Part V: The Part of Tens
Answer: Working backward, the 8 bars that remained must have been twothirds of what was there when the third pirate did the splitting up. So the third
pirate saw 12 bars,
Chapter 18: Plying Pythagoras
7
Figure 18-8:
Katie lands
x miles
down the
coast.
32
32 x
x
6
Find the two distances along the hypotenuses (in terms of x) using the
Pythagorean theorem. After finding t
Chapter 18: Plying Pythagoras
and letting a = 36 and c = 39, the equation reads 362 + b2 = 392. Simplifying, you
get 1,296 + b2 = 1,521. Subtract 1,296 from each side, and you find that b2 = 225.
Taki
Chapter 19: Going around in Circles with Perimeter and Area
Table 19-2
Comparing Sizes of Posters
Printed
Height
Printed
Width
Height + 6
Width + 4
Total Area
40
3
46
7
322 square inches
30
4
36
8
288
Chapter 19: Going around in Circles with Perimeter and Area
Determining the area around the outside
When you have an existing pool or other area that needs to be surrounded,
then you take measurements
Chapter 19: Going around in Circles with Perimeter and Area
Having a nice, rectangular pasture or yard is fine and dandy, but what if you
need to keep the little boy sheep separated from the little gi
Chapter 18
Plying Pythagoras
In This Chapter
Applying the Pythagorean theorem to everyday situations
Mixing it up with rates and times in a right triangle
Using more than one right triangle to solv
Chapter 18: Plying Pythagoras
The rate at which he can row is different from the rate at which he can walk.
Where he comes ashore affects how far he rows and how far he walks. In
Figure 18-6, you see
Chapter 18: Plying Pythagoras
Determining Distances between Planes
Planes travel at different speeds and different heights. A traffic controller has
the responsibility of keeping the planes a safe dis
G
In this part . . .
eometry: You either love it or hate it. Geometry word
problems really are your friends. They almost always
involve a formula that you insert and then solve. The main
challenge to
260
Part IV: Taking the Shape of Geometric Word Problems
The quadratic equation can be factored, but the factors arent easy to come
by. Using the quadratic formula, while messy, is quicker in this cas
Chapter 19
Going around in Circles
with Perimeter and Area
In This Chapter
Computing the perimeter and area of polygons
Coming full circle with the circumference and area of a circle
Putting shapes
254
Part IV: Taking the Shape of Geometric Word Problems
Finding the height of a window
How tall is the window in a building? You cant go inside the building to take
the measurements, but you have inf
272
Part IV: Taking the Shape of Geometric Word Problems
The regular hexagon is made up of six equilateral triangles; the sides of
each of the triangles is 6 inches. Use Herons formula to find the are
252
Part IV: Taking the Shape of Geometric Word Problems
Finding the Height of an Object
You measure your own height with a tape measure or yardstick, and you measure the walls in a room by standing o
282
Part IV: Taking the Shape of Geometric Word Problems
Just how large a rectangle will fit into a circle, if you have some particular
constraints?
The Problem: You want to fit a rectangle with lengt
274
Part IV: Taking the Shape of Geometric Word Problems
The four corners of the walkway are each one-fourth of the same 6-footradius circle. Just find the area of a circle with a radius of 6 feet, an
264
Part IV: Taking the Shape of Geometric Word Problems
The Problem: The tide is moving out at a rate of 2 feet per second. The height
difference between where a rope is connected to the dock and the