Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Algebra

Hi, can anyone please give me a few practice questions similar to:

One integer is 5 more than twice another integer.
The squares of these two integers have a difference of 312.

Integers are ______ and _______

It would be really helpful if u can show full explanations aswel, thanks so much if someone could do this!!!!

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Algebra

Integers are ___fun___ and ___exciting___

Questions are much easier to handle in math once you have equations:

One integer is 5 more than twice another integer.
The squares of these two integers have a difference of 312.

x = 5+2y
x^2 - y^2 = 312

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

polylog

Member

Registered: 2006-09-28

Posts: 162

Re: Algebra

There are two integers.

The difference between twenty-five times the first integer and the second integer is five.

Four times the square of the first integer is equal to one-fifth of the second integer.

What are the integers?

SOLUTION
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The sentences translate to these eqautions:

25x - y = 5    .. (1)

4x^2 = (1/5)y  .. (2)

Re-arranging (1) :

y = 25x - 5

Substituting this into (2) :

4x^2 = (1/5)y

4x^2 = (1/5)(25x - 5)

4x^2 = 5x - 1

4x^2 - 5x + 1 = 0

Applying quadratic formula:

x = [5 (+/-) sqrt(25 - 4*4*1) ]/8

   = (5 + 3)/8

   = 1

   (reject 2/8 since we are looking for integers!)

Now using re-arranged (1) :

y = 25x - 5
   
   = 25 - 5

   = 20

So the two integers are 1 and 20.

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: Algebra

Thanks alot polylog! These are excellence questions in my end of year exam for algebra(pretty easy) but i just wanted to make sure i knew the stuff. Thanks again polylog!!

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei