Algebra quadratic formula word problem

**lightstevoo** · January 18th 2010, 01:11 PM

I have two problems I am new here and I want to see how this site works...
so...
#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.

2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.

**General** · January 18th 2010, 01:24 PM

Originally Posted by lightstevoo

I have two problems I am new here and I want to see how this site works...
so...
#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.

2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.

Try to obtain equations from your problems.
For the first one:
Let a be the first number, and b be the second number,
thier sum = 5 $\implies a+b=5 .... (1)$
thier product = 5 $\implies ab=5 .... (2)$
Now, If we subtract a from the both sides in equation (1), we will get:
$b = 5 - a .... (3)$
By substituting (3) in (2), we get:
$a(5-a)=5$
$5a-a^2=5$

Now, Solve the last quadratic equation for a.
Once you have the values of a, substitute them in (3) to obtain the value of b.
Do not remember to reject the negative values; because the question said that : the two numbers are positive.

I will leave the second for you.
Try to obtain some equations from it.

**pickslides** · January 18th 2010, 01:29 PM

Hi there lightstevoo, welcome to MHF!

Originally Posted by lightstevoo

I have two problems I am new here and I want to see how this site works...
so...

On this forum we try to 'help' you solve the problem not just solve it for you.

Originally Posted by lightstevoo

#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.

Lets say your numbers are $x$ and $y$ . From the problem

$x+y = 5$

and

$x\times y = 5$

The first statement can be writtien as

$x = 5-y$

Lets use that to put into the secons statement which becomes

$(5-y)\times y = 5$

Now you need to exapnd this and solve

$5y-y^2 = 5$

Have a go from here

Originally Posted by lightstevoo

2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.

This is similar to the first

Lets call the $x$ the length and $y$ the width. As one side (lets call it the width of your triangle) of your rectangle is the barn then only 3 sides need to be fenced.

So you have

$x+x+y= 100$

and

$x\times y = 1200$

The first statement can be writtien as

$2x+y= 100$ then $y= 100-2x$

Can you take it from here?

**Archie Meade** · January 18th 2010, 01:31 PM

Q1.

$(x-a)(x-b)=x^2-(a+b)x+ab=x^2-5x+5$

$a\ and\ b\ are\ \frac{5+\sqrt{25-20}}{2}\ and\ \frac{5-\sqrt{25-20}}{2}$

Q2.

The barn side dimensions are

$x,\ 50-\frac{x}{2}$

Use the area to solve for x.

**lightstevoo** · January 18th 2010, 01:52 PM

i got the answer thanks to you guys

so ㅡㅡㅡ ㅡ ㅡ ㅡ
l l
x l l x
l l
l l
ㅡ ㅡ ㅡ ㅡ ㅡ ㅡ
100-2x

(100-2x)x= 1200
x^2-50x+600
and then you do the quadratic formula.
then you get the answers
20, and 30
then you plug it in
FINAL ANSWERS
30,40
20, 60

thank you!

**lightstevoo** · January 18th 2010, 01:53 PM

yes and i got it thank you!
emm
the answer is
5 plus or minus radiacal 5 /2

**Archie Meade** · January 18th 2010, 02:28 PM

I hope my pen dimensions were not confusing, lightstevoo.

My x was the side against the barn.

**Jameson** · January 18th 2010, 02:29 PM

Originally Posted by lightstevoo

yes and i got it thank you!
emm
the answer is
5 plus or minus radiacal 5 /2

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