one number is 4 times another. if the sum of their reciprocals is 1/8, find the two numbers.?

Question

please help

Answer 1

Let x = "One number". Then the other number is x/4. That makes their reciprocals 1/x and 4/x, respectively. So

1/x + 4/x = 1/8 ==

5/x = 1/8 ==

5 = x/8 ==

40 = x = the first number, so the other number is x/4 = 10

Answer 2

Let x and y be the numbers you are looking for. Now, you know that one number is 4 times the other number, so you can say:

x = 4y

Also, you know their reciprocals add up to equal 1/8, so

1/x + 1/y = 1/8

Now, you can substitute x with 4y in the above equation:

1/4y + 1/y = 1/8

Now, find a common denominator for the left side of the equation. The best common denominator is 4y:

1/4y + 4/4y = 1/8
5/4y = 1/8

Now, cross multiply:

4y(1) = 5(8)
4y = 40
y = 10

Since you know that x = 4y, and you now know that y = 10, solve the equation to find x:

x = 4y
x = 4(10)
x = 40

So, x = 40 and y = 10

Answer 3

10 and 40, by trial and error. I know that one of the numbers has to be slightly larger than 8 in order for its reciprocal to be slightly less than 1/8 (we want it to be less so that we can another very small fraction to it to sum to 1/8). I noticed that 1/10 and 1/40 can be written as 4/40 and 1/40 whereas 1/8 is 5/40. Done.

Answer 4

let one of the numbers be x. The other is 4x.
1/x+1/4x=1/8
(4+1)/x=1/8
(5/4)x=1/8
cross multiply
40x=4
x=40/4=10
The number is 10 and 40 (4 times 10)
Check: 1/10+1/40=(4+1)/40=5/40=1/8

Answer 5

Cute problem.

A) x = 4y
B) 1/x + 1/y = 1/8

Substituting A into B we get: 1/4y + 1/y =1/8

Multiply both sides by 8y: 2 + 8 = y

So y = 10 and by equation A: x = 40

Answer 6

Let, one number = x
The other number = 4x

1/x + 1/4x = 1/8

Multiply throughout with 8x:
8 + 2 = x
x = 10

The other number = 4 * 10 = 40

Therefore, the two number are: 10 and 40

Answer 7

y - one of the numbers.
x - one of the numbers.

4x = y

1/y + 1/x = 1/8
But 4x = y,
→
1/4x + 1/x = 1/8
(¼ + 1)/ x = 1/8 (Spin around).
(5/4) / x = 8/1
5/4 * 8/1 = x
40/4 = x
x = 10

4x = y
4(10) = y
40 = y


Now check answer:
1/y + 1/x = 1/8
1/40 + 1/10 = 1/8
5/ 40 = 1/8
1/8 = 1/8

And 40 is four times greater then 10.

Answer 8

Solve:
x = 4y
1/x + 1/y = 1/8

Use substitution:
1/(4y) + 1/y = 1/8
¼*(1/y) + 1/y = 1/8

I hope you continue this one to get y. Then get x.
Please try to do this on your own by this time as your practice.


Hey, the correct answers are 10 & 40.
d:

Answer 9

the answer is 1/1.6

X+X*4 can be thought of as
8 = 5/y

Therefore 8/5 = 1.6

Answer 10

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2 and 4.

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