These problems will be used to prepare for a test, so they are need
ASAP!

Situation #1:
Andrew was driving home from school one day and decided to stop for a
slice of pizza.  He went to Pizza Pizzazz, a pizzeria owned by his
best friend Joe.  Joe was happy to see Andrew because, on this day,
Joe's delivery person had called in sick and Joe had a stack of pizzas
to get out to his customers.  Andrew was delighted to help his friend,
and after he feasted on  a variety of delicious slices, Andrew packed
the stack of pizzas in his car, grabbed the delivery list, and drove
away.
He delivered one-sixth of the pizzas to the first address, and
one-fifth of the remaining pies to the next address.  On his third
stop, Andrew delivered one-fourth of the remaining pies; on the next
stop, one-third; and on the next, one-half.  He delivered the
remaining 5 pizzas to the last address.
How many pizzas did Andrew begin with?

Situation #2
Chris, Max, Paul, and Ryan own Splash Down, a white water rafting
company on the banks of the Swallowme and Quicksink Rivers.  The
Swallowme River runs directly north and south, and the Quicksink River
runs directly east and west.  These rivers cross at the center of the
white water trail and divide the area into four quadrants.  The only
paths for rafting are directly on the north to south river and on the
east to west river.  Chris, Max, Paul, and Ryan would like to expand
the paths to three more located in the northeast quadrant, where the
rapids run fast and furious.  They feel it would be a challenging ride
for those brave hearts.
White water trail A would run from a point 300 meters north of the
origin to a point 400 meters east of the origin.
Trail B is to begin at a point 100 meters north of the origin and
follow a line that travels 3 meters north for every 7 meters it
travels east intil it meets trail A.
Trail C is to run from the origin to trail A in such a way that it
exactly bisects the area in the northeast quadrant that is south of
both trail A and Trail B.
The owners of Splash DOwn have asked your help in providing them with
some pertinent information.
You are to provide the equations of the three proposed white water
rafting trails, as well as the exact location (coordinates) where
trail B meets trail A and where trail C meets trail A.

For both situations, be sure to provide explanations and organized
work.  Include maps, charts, or any other visuals that may help me to
understad this problem.

These problems will be used to prepare for a test.

Thanks !

Hi bildy!!!

Situation #1:

If we call T the total amount of pizzas delivered by Andrew we have
for the first delivery:
He deliver 1/6*T and then remains 5/6*T to deliver.

Second delivery:
Deliver 1/5*(5/6*T))=1/6*T , then remains 4/6*T to deliver.

Third delivery:
Deliver 1/4*(4/6*T)=1/6*T , then remains 3/6*T to deliver.

Fourth delivery:
Deliver 1/3*(3/6*T)=1/6*T , then remains 2/6*T to deliver.

Fifth delivery:
Deliver 1/2*(2/6*T)=1/6*T , then remains 1/6*T to deliver.

For the last delivery he has 5 pizzas, then 
1/6*T = 5 ==> T = 5*6 = 30 pizzas.

Andrew begun with 30 pizzas.

                 ---------------- xxx ----------------

Situation #2:

Here I must work inthe way that I interpreted the problem, the
problemīs statement is a little obscure; but if we consider the the
two rivers as the coordinates axis x and y of the plane ( axis y for
the north to south river and axis x for the east to west river). The
origin is the point where the two rivers are crossed (the intersection
of the x- and y-axis), and the northeast quadrant is the first
quadrant of the plane (where x and y are both positive).

Trail A:
It starts at the point (0,300) and ends in the point (400,0).
Here we can follow to ways to determine the trail A, we can use the
Slope y-intercept form or the Two point form.

-Slope y-intercept:
y = m x + b, if m is finite.

When x = 0 , y = 300 and y = b, then b = 300.
When y = 0 , x = 400 and m = -b/x = -300/400 = -3/4.
Then the equation for the line containing the trail A is y = -3/4 x +
300 .

-Two point form:
Given two points, P1=(x1,y1) and P2=(x2,y2), the equation of the line
that contains the two points is:
(x-x1)(y2-y1) = (y-y1)(x2-x1)

Here P1=(0,300) and P2=(400,0) , then:
(x-0)(0-300) = (y-300)(400-0) ==> -300 x = 400 (y-300) ==> y-300 =
-300/400 x
==> y = -3/4 x + 300 .

The trail A comprises only the segment between P1 and P2, 
such is for 0 =< x =< 400 .

-----------------------------------

Trail B:
Here we have a point P =(0,100) and (in some way) the slope m.
Let the slope of the line be m, if the inclination of a line is alpha
then
tan(alpha)= m . from this definition it is easy to see if we know how
varies y due a variation of x or viceversa that m = (variation of
y)/(variation of x);
in this case when we move 3 meters to the north (variation of y) we
move also 7 meters to the east (variation of x), then:
m = 3/7 .

We can use the -Slope y-intercept form:
y = m x + b, when x = 0 y = 100 and y = b , then b = 100.
So
y = 3/7 x + 100 .

Or we can use the Point slope form:
y - y1 = m(x-x1), if m is finite.

In this case (x1,y1) = (0,100) and m = 3/7 , then:
y - 100 = 3/7 (x - 0) = 3/7 x ==> y = 3/7 x + 100 .

Now we know when the trail starts (when x=0), but not when it ends.
It happens when the line meets the trail A, it is when both trail A
and trail B equations are satisfied:

-3/4 x + 300 = 3/7 x + 100 ==> 3/7 x + 3/4 x = 300-100 = 200 , then
33/28 x = 200 ==> x = 5600/33 ,
y = 3/7 x + 100 = 3/7 5600/33 + 100 = 800/11 + 100 = 1900/11 .
The meeting point is (5600/33,1900/11).
And the equation for the trail B is:
y = 3/7 x + 100    0 =< x =< 5600/33 .

-------------------------------

Trail C:

First of all we must calculate the area K in the northeast quadrant
that is south of both trail A and Trail B:
We have a plygon whose vertices are:
P1 = (0,0)              origin
P2 = (0,100)            start point of trail B
P3 = (5600/33,1900/11)  meeting point of trails A and B [aprox
=(169.7,172.7)]
P4 = (400,0)            end of trail A

We can use the expression:
The area of a polygon whose vertices are P1, P2, .., Pn is 
K = [(x1y2 + x2y3 + x3y4 + ... + xny1) - (x2y1 + x3y2 + x4y3 + ... +
x1yn)]/2

and we have K = 1,420,000/33 .

Now we know that one of the possibilities for the trail C will form a
triangle whose vertices are the origin, the meeting point of trails C
and trail A and the end of trail A. We will work with this, if we get
an answer here, the problem is solved.
The area T of this triangle will be:
T = K/2 and
T = Base * High / 2 = 400 * H / 2
then
400*H = K ==> H = K/400 = (1,420,000/33)/400 = 3550/33 .
The high of this triangle is the y-axis value of the meeting point of
this trail with the trail A. The value obteined is less than the
y-axis value of the meeting point of the trails A and B, then this
trail is the correct one (that means the trail C donīt meet trail B
and the figure of the triangle used is correct, in other case, the
polygon is a quadrilateral).
Now we have the y-axis value of the meeting point of trails A and C,
then the x-axis value can be calculated using the equation of the
trail A:

3550/33 = -3/4 x + 300 ==> 3/4 x = -3550/33 + 9900/33 = 6350/33 ==>
x = 25400/99

The meeting point of trails A and C is (25400/99,3550/33).

We need to find the equation of trail C. We have two points, the
origin and the meeting point with trail A.
We can use the Two point form:
(x-x1)(y2-y1) = (y-y1)(x2-x1)
(x-0)(3550/33-0) = (y-0)(25400/99-0) then
3550/33 x = 25400/99 y   then
y = 3550/33 . 99/25400 x = 213/508 x

The equation for trail C is:
y = 213/508 x       0 =< x =< 25400/99

-----------------------------------------

You will find useful the following page:
"Analytic Geometry Formulas" from DrMath.com:
http://drmath.com/dr.math/faq/formulas/faq.ag2.html

It is not possible to post a math graph here, but i think that the
explanations lead you to do the graph by yourself easily. If you still
have troubles with this, please let me know and I will try to find a
way to made the graphs availables to you.

I hope this helps you. Remember that if you think that the problem was
misunderstood by me, there are missing points, or need a clarification
please post a request for an answer clarification. I will be glad to
respond your requests. Please also let me know how this answer works,
and consider the fact that it be possible to find errors in
calculations (I checked them but...)but the most important thing here
is the showing of the way to solve the problems.

Best regards.
livioflores-ga

The answers to some of the questions were incorrect / unsatisfactory. 
The answer to #1 was fine, probably since it was the easier of the two
problems by far, but the answer to #2 was completely off.  I can
verify this through information from several other professional
sources.  I look forward to having a more positive experience with
google answers in the future, as I have oh so many times in the past.

Question 1 is very easy - he started with 30 pizzas.

1/6 of 30 = 5
1/5 of 25 = 5
1/4 of 20 = 5
1/3 of 15 = 5
1/2 of 10 = 5
5 are left