Monday

December 22, 2014

December 22, 2014

Posted by **jasort20** on Wednesday, March 14, 2007 at 2:52am.

one number is 2 times another. If the sum of their reciprocals is (1)/(4). Find the two numbers.

We can begin by looking at the following. Let's use the letters "a" and "c.":

"One number is 2 times another."

c=2a (c is 2 times larger than a here)

"the sum of their reciprocals is 1/4"

"The sum" is a fancy term them mathmaticians use to say "if you add them up, you get this number." So we know we're adding.

Read this next paragraph carefully. I'm going to explain a lot. Just make sure you understand every sentence or it will not make sense. If you get lost and you read it carefully, at least you'll know what part you were lost on and can ask about that part.

Reciprocal is when you flip a number's fraction. So if you take 2/3, the reciprocal is 3/2. In the case of numbers that we don't write a denominator for (such as 2, 5, 100, 1958069384, etc.), the denominator is 1. Why? Because if we divide ANYTHING by 1, we end up with the same amount.

So our fractions for our "c" and "a" numbers are c/1 and a/1. But we're looking to flip them in this problem, so we end up with 1/c and 1/a. Those 2 add up to 1/4. So now we have:

1/c + 1/a = 1/4

Since c = 2a (what we came up with first), we can plug that in to this equation.

1/2a + 1/a = 1/4

Now we have to get a common denominator. If we multiply (1/a) by 2/2, we get:

1/2a + 2/2a = 1/4

On the left, we add 1/2a and 2/2a and get :

3/2a. Now, we see that

3/2a = 1/4.

Can you solve for "a" and figure out what the 2 numbers are they're asking about? (Still leaving a little for you to do). :)

Matt

Let me know if this is correct

3/2a=1/4

to solve for a

a = 0.2 or 1/5

is this correct...

No, that's wrong...did you multiply 1/4 and 3/2a by 2/3?

3/2a = 1/4

There are a few ways you can do that. Let's start by dividing both sides by 3/2a. (Or multiplying by 2a/3)

1=2a/12

Now, we know we can multiply both sides by 12. That is 1*12 = 12(2a/12)

On the right side, the 12s cancel. So you have

12=2a

Divide each side by 2 to get "a" by itself.

6=a

So one answer is 6. The other formula is c=2a. So the other number is 12.

6 and 12 :)

Matt

**Answer this Question**

**Related Questions**

algebra - One number is 4 times another. If the sum of their reciprocals is 5/36...

Algebra - One number is 3 times another. If the sum of their reciprocals is 4, ...

algebra - One number is 5 times another If the sum of their reciprocals is 2/15 ...

math - Last one, The sum of two numbers is 48. Four times the smaller number is ...

college - One Number Is 3 Times Another Number. If The Sum Of The Reciprocals Of...

Math - Can someone please help me write this statement out in formula form. ...

math - can someone help me on this question ive been stuck on it for almost an ...

Algebra - One number is 6 more than another. If the sum of the smaller number ...

math - Two numbers are reciprocals of each other. One number is 9 times as large...

Grade 8 Math - Can you write them in Mathematical/numbers form I'll solve them ...