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October 27th, 2010, 01:15 AM   #1
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Find two numbers where difference is 20 & the sum is -4

Find 2 numbers such that the difference between them is 20 and their sum is -4.

Is there a systematic way or method to solve this besides just guessing integers?

(p.s. No algebra allowed, this is a pre-algebra questions)
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October 27th, 2010, 01:34 AM   #2
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Re: Find two numbers where difference is 20 & the sum is -4

Quote:
Originally Posted by sharp
...Is there a systematic way or method to solve this besides just guessing integers? ...
Yes...it's called algebra.

However, we know one number is positive and the other is negative since their difference is greater than their sum. And since their sum is -4, the negative number is 4 units farther from zero than the positive number, and the sum of their distances from zero is 20. So, we can ask ourselves, what two numbers add up to 20 whose difference is 4. It should be easy to see we need 12 and 8. So the two numbers we need are -12 and 8.
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October 27th, 2010, 02:55 AM   #3
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Re: Find two numbers where difference is 20 & the sum is -4

Yeah...,I think you're right,MarkFL.
The answer is -12 and 8,that's right.But your solution is quite too long.I have a shorter solution.
I have no time now,so I can't post it.But I'll post it soon.
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October 27th, 2010, 01:43 PM   #4
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Re: Find two numbers where difference is 20 & the sum is -4

x-y=20
x+y=-4
add to get 2x=16 or x=8 and y=-12
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October 27th, 2010, 03:38 PM   #5
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Re: Find two numbers where difference is 20 & the sum is -4

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However, we know one number is positive and the other is negative since their difference is greater than their sum.
What?!? I don't get this at all.
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October 27th, 2010, 04:06 PM   #6
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Re: Find two numbers where difference is 20 & the sum is -4

What I should have said is the magnitude of the difference is greater than the magnitude of the sum. The magnitude of a number is simply its distance from zero, or its absolute value. For the three scenarios below, we will use the positive numbers x and y to illustrate, where x > y.

Take any two positive numbers. Wouldn't you agree that their sum will be greater than the magnitude of their difference?

x + y > x - y

Add y - x to both sides.

2y > 0

Divide through by 2.

y > 0

Since we defined y to be positive, this has to be true.

Take any two negative numbers. Wouldn't you agree that the magnitude of their sum will be greater than the magnitude of their difference?

|(-x)+(-y)| > |(-x) - (-y)|

|-1||x + y| > |-1||x - y|

Since |-1| = 1 and x > y, we have

x + y > x - y

Same as above.

Now take a positive number and a negative number. The magnitude of their sum is equivalent to the magnitude of their difference if the negative number was positive, and the magnitude of their difference is equivalent to the magnitude of their sum if the negative number was positive, so the magnitude of their difference will be greater than the magnitude of their sum.

|x + (-y)| < |x - (-y)|

|x - y| < |x + y|

Since x > y, we have

x + y > x - y

Same as above.
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October 30th, 2010, 05:20 AM   #7
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Re: Find two numbers where difference is 20 & the sum is -4

Wow,MarkFL and mathman...
That's what I said.
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October 30th, 2010, 08:52 AM   #8
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Re: Find two numbers where difference is 20 & the sum is -4

Uh... WHAT?!? It's too early in the day to be hallucinating
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