You are watching: What two numbers add to make twenty and have a difference of four?
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)
Yes...it"s called algebra. :mrgreen: 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.
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.
However, we know one number is positive and the other is negative since their difference is greater than their sum.
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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 - yAdd y - x to both sides.2y > 0Divide through by 2.y > 0Since 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 havex + y > x - ySame 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| Since x > y, we havex + y > x - ySame as above.