Math gods....need help with word problems

[Cooljt1]

now most of these problems i can solve but what i can't get is the algebraic equation to represent it.

1. two positive integers differ by 3, and their product is 108. Find the numbers.

2. Find two numbers such that their sum is 10 and their product is 22.

3. Suppose that the sum of two whole numbers is 9 and the sum of their reciprocals is 1/2. Find the numbers.

4. The sum of the lengths of two legs of a right triangle is 21 inches. If the length of the hypothenuse is 15 inches, find the length of each leg.

5. A rectangular plot of ground measuring 12 meters by 20 meters is surrounded by a sidewalk of a uniform width. The area of the sidewalk is 68 square meters. Find the width of the walk.

 

[Kelemvor]

You just have to set each one up as 2 equations and then solve for one letter...

E.G.

1)
X-Y=3
XY=108 -> Y=108/X
Combine the two to get X-(108/X)=3
Then get your standard quadratic by multiplying by X
X^2 - 3X - 108 = 0

2)
X+Y = 10
XY=22 -> Y=22/X
Combine = X + 22/X = 10
Quadratic = X^2 - 10X + 22 = 0

Same basic idea for the rest I would guess but too lazy to read them

OK I'll read them.

3) Ick, reciprocals are ugly

4)
X^2 + Y^2 = 15^2
X+Y=21 --> Y=21-X
Combine to Quad (don't quote me on this one) --> 2X^2 - 42X + 216 =0

5)
Area of ground = 12 * 20 = 240
Area of sidewalk and land = (12+X) * (20+X)
Area of sidewalk only = (12+X) * (20+X) - 240
Combine to Quad (Been a looong time...) X^2 + 32X

Man, have't done this stuff in 10+ years so I can vouch for any of this. heh heh.

 

[minendo]

What is this? 9th grade Algebra?

 

[Francesca]

These are slight guesses so sorry, but I thought I'd try for fun.

1. x(x+3)=108

2. So way off on this one, but I'm having fun being weird.... x(10-x)=22

3. Yeah, I'm not even attempting anything that uses the word 'reciprocal'.

4. This is pathagorean theorum so a^2 +b^2=c^2 so 15^2=a^2+b^2 when a+b=21

5. My brain hurts now.

Hey, good luck. Sorry I'm not the miracle math goddess you were searching for.

 

[Francesca]

Originally posted by: FrankyJunior
You just have to set each one up as 2 equations and then solve for one letter...

E.G.

1)
X-Y=3
XY=108 -> Y=108/X
Combine the two to get X-(108/X)=3
Then get your standard quadratic by multiplying by X
X^2 - 3X - 108 = 0

2)
X+Y = 10
XY=22 -> Y=22/X
Combine = X + 22/X = 10
Quadratic = X^2 - 10X + 22 = 0

Same basic idea for the rest I would guess but too lazy to read them

Now there is the math god....

 

[RaynorWolfcastle]

1 - x-y=3, xy=108 , x & y > 0
2 - x+y = 10, xy=22
3 - x+y=9, 1/x + 1/y = 1/2, x&y belong to Z
4 - suppose you have triangle with sides x,y,z where z is the hypotenuse. x+y = 21", z= 15", solve for x & y
5 - Try to figure this one out yourself, I won't solve them all for you

 

[SammyBoy]

mad easy man. read the book or use common sense please!

 

[Mean MrMustard]

Here is the answer.

 

[Cooljt1]

common sense...ehhh....not so common i guess....i already have the answers for all these problems but just needed help to get the algebraic equations. i can do math equations fine but word problems i totally suck at and can never figure out the equation to work it out.