## One number is 6 times another. The sum of their reciprocals is 7/24. find the numbers

Question

One number is 6 times another. The sum of their reciprocals is 7/24. find the numbers

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1 week 2021-10-05T03:43:22+00:00 2 Answers 0

The numbers are 4 and 24

Step-by-step explanation:

Let the first number be and the second number be .

since we were told that one number is 6 times another , let

x = 6y ……………………………. equation 1

The reciprocal of The reciprocal of The sum of the reciprocal will therefore be : …………………………….. equation 2

substitute into equation 2 , equation 2 then becomes : The L.CM is 6y ,

then we have  since they have the same numerator , we will equate the denominator , that is divide through by 6 substitute into equation 1 to find the value of x , that is  Therefore : The numbers are 4 and 24

Check:    L.C.M = 24

so we have = x=24, y=4

Step-by-step explanation:

x=6y

1/x+1/y=7/24,

1/6y+1/y=7/24

1/6y+6/6y=7/24

(1+6)/6y=7/24

7/6y=7/24, then

6y=24

y=24/6

y=4

x=6y=6*4=24