i just need help with three word problems

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tarheel2006

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Joined
Dec 3, 2008
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14
Avoiding a collision. A car is traveling on a road that
is perpendicular to a railroad track. When the car is
30 meters from the crossing, the car’s new collision
detector warns the driver that there is a train 50 meters
from the car and heading toward the same crossing. How
far is the train from the crossing?

Winter wheat. While finding the amount of seed needed
to plant his three square wheat fields, Hank observed that
the side of one field was 1 kilometer longer than the side
of the smallest field and that the side of the largest field
was 3 kilometers longer than the side of the smallest field.
If the total area of the three fields is 38 square kilometers,
then what is the area of each field?
So far with this I have
Smaller=x
next field=x+1
larger=x+3

Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 + r)2
27,000.
 
tarheel2006 said:
Avoiding a collision. A car is traveling on a road that
is perpendicular to a railroad track. When the car is
30 meters from the crossing, the car’s new collision
detector warns the driver that there is a train 50 meters
from the car and heading toward the same crossing. How
far is the train from the crossing?

Winter wheat. While finding the amount of seed needed
to plant his three square wheat fields, Hank observed that
the side of one field was 1 kilometer longer than the side
of the smallest field and that the side of the largest field
was 3 kilometers longer than the side of the smallest field.
If the total area of the three fields is 38 square kilometers,
then what is the area of each field?
So far with this I have
Smaller=x
next field=x+1
larger=x+3

Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 + r)2
27,000.
Click to expand...

On the first one, did you draw a right triangle and label it according to the words of the problem? The next step is to use the Pythagorean Theorem.

On the second one, you are correct so far. You know that the area of a square is the square of one side. Build your equation on the fact that the areas of the three fields, when added together, total 38.

I guess the equal sign went missing in the third one. I'll guess that the equation you are asked to solve is 12,000(1+r)[sup:1jjop0po]2[/sup:1jjop0po]=27,000.
Your first step is to eliminate the parenthesis by squaring "1+r" and multiplying the result by 12,000. Then get everything on the left side of the equation with zero on the right side. Factor the left side and solve. If it is not factorable, use the quadratic formula.

If you need more help, show us your work and tell us where you are stuck.
 
tarheel2006 said:
Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 + r)2
27,000.
Click to expand...

\(\displaystyle 12000(1+r)^2 \, = \, 27000\)

Loren gave you the most general way to solve the problem.

But for this problem, fastest way to solve would be to (because of the numbers involved):

divide both side by 12000 and reduce the fraction

take square-root of both sides and solve.
 
Ok on the last one I came up with some odd stuff, so here's what i got 2 ways
1)12000-12000r2=27000
-12000r2+12000=27000
-12000=-12000
-12000r2=15000
-12000 -12000
r2=5/4

2)12000-12000r2=27000
-12000r2+12000-27000=0
-12000r2-15000=0
should i factor this out to =0
-3000(2000r- ) (r
 
tarheel2006 said:
Ok on the last one I came up with some odd stuff, so here's what i got 2 ways
1)12000-12000r2=27000
-12000r2+12000=27000
-12000=-12000
-12000r2=15000
-12000 -12000
r2=5/4

2)12000-12000r2=27000
-12000r2+12000-27000=0
-12000r2-15000=0
should i factor this out to =0
-3000(2000r- ) (r
Click to expand...

Both the ways you have shown is wrong at the first step. The correct expansion of (1+r)^2 is:

\(\displaystyle (1 \, + \, r)^2 \, = \, 1 \, + 2\cdot r \, + \, r^2\)

You missed the '2r' term.

What level of math are you doing? What Grade are you in? I am asking because that will tell me what you should have known and need to review.
 
I am in college alegebra at the age of 36. so its been a long time. the word problems are killing me but everything else in the class is great.
 
tarheel2006 said:
Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 + r)2
27,000.
Click to expand...

Quick way to do the problem above:

\(\displaystyle 12000(1+r)^2 \, = \, 27000\)

\(\displaystyle (1+r)^2 \, = \, \frac{27000}{12000}\)

\(\displaystyle (1+r)^2 \, = \, \frac{9}{4}\)

\(\displaystyle (1+r)^2 \, = \, (\frac{3}{2})^2\)

\(\displaystyle 1 \, + \, r \, = \, \frac{3}{2}\)

\(\displaystyle r \, = \, \frac{3}{2} \, - \, 1\)

\(\displaystyle r \, = \, \frac{1}{2} \,\)

r = 50%
 
so is it where i factor out 3000
3000(4000r2+8000r-5000)=0
3000(2000r-1)(2000r+5)=0
2000r/2000=1/2000


2000r-5=0
+5= +5
2000r/2000=5/2000
=1/4000???
 
Dag, I didn't know someone done it for me. NOW I feel DUMB. So on my last attempt was I even close?
 
tarheel2006 said:
so is it where i factor out 3000
3000(4000r2+8000r-5000)=0

If you "multiply out" the above - would you get back the original solution? I would say - no. It should be as follows:

3000(4r^2 + 8r -5) = 0

(2r - 1)(2r + 5) = 0

Then either

2r - 1 = 0

2r = 1

r = 1/2

or

2r + 5 = 0

2r = - 5

r = - 5/2 ......................not probable - because r is positive

so the correct answer

r = 1/2 or 50%

3000(2000r-1)(2000r+5)=0
2000r/2000=1/2000


2000r-5=0
+5= +5
2000r/2000=5/2000
=1/4000???
Click to expand...
 
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