Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 429

6. A pizza’s shape is circular so we need the area formula for a circle which
   is A = or^2. The radius is half the diameter, so the restaurant’s large
   pizza has a radius of 8 inches. The area of the restaurant’s large pizza
   is o(8)^2 = 64o ≈ 201. The restaurant’s large pizza is 20% larger than the
   competition’s large pizza. Let A represent the area of the competition’s
   large pizza. Then 201 is 20% more than A:
   201 0201020120
   201 120
   201
   120
   16

=+ =+ =

=

=

AAAA

A

A

.(.).

775

1675

1675

1675

73

2

2

2

= = = = = ≈

A

Ar

r

r

r

r

o

o

o

o

The competition’s radius is approximately 7.3 inches, so its diameter is

approximately 2(7.3) = 14.6 inches.

Distance Problems

There are several distance problems that quadratic equations can help us solve.
One of these types is the “stream” problem. In this type of problem, a vehicle
travels the same distance up and back; in one direction, the “stream’s” average
speed is added to the vehicle’s speed, and in the other, the “stream’s” average
speed is subtracted from the vehicle’s speed. Another type involves two bodies
moving away from each other where their paths form a right angle (for instance,
one travels north and the other west). Finally, the last type is where a vehicle
makes a round trip that takes longer in one direction than in the other. In all of
these types, the formula D = rt is key.