can someone explain to me the following:thanks...
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