Question 288281: One Number Is 3 Times Another Number. If The Sum Of The Reciprocals Of The Numbers Is 1/6, What Are The Two Numbers? Found 2 solutions by amnd, Grinnell:Answer by amnd(23) (Show Source):
You can put this solution on YOUR website! Say that one of the number is A, and the other is B.
A is three times the other number:
A = 3B
The reciprocal of a number is another number which, if multiplied by that number, would yield 1. The reciprocal of A would be 1/A, and the reciprocal of B would be 1/B.
First, finding the value of B:
This would yield:
Therefore, B = 8
Therefore, A = 24
You can put this solution on YOUR website! The key here is setting up the unknowns. AND,
of course translating the English to the Math.
Our two mystery numbers are x and 3x. Stop here to
make sure why this is true. OK
now the reciprocals
1/x+1/3x=1/6
Let's remove those messy fractions, shall we?
We will multiply by (x)(3x)and(6)
we get 3x^2-18X-6x=0
Let's pull the 3x out.
3x(x-6-2)=0
Solutions are zero and 8.
well for our purposes zero will not work. Big Mama said a number divided by zero is undefined--actually infinite--but that is another lesson.
Sooo, let's try 8, shall we?
1/8+1/24=3/24+1/24=4/24=1/6. The answer is 8. Big Mama told me to go to bed. But wait, we have not satisfied what Big mama wanted!!!! If x is eight, then the other number is 3x which is then 24. Another lesson here is that you go back to the the actual problem and be clear on what the problem is asking for. Big mama wants TWO numbers. So the answer to the problem is 8 AND 24. ALWAYS GO BACK TO THE PROBLEM TO MAKE SURE YOU SATISFY WHAT BIG MAMA WANTS. You don't want to upset her. AND, you don't want points taken away on a test because you partially solved the problem.
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