SOLUTION: One number is 4 times as large as another. The sum of their reciprocals is 35/4. Find the two numbers.

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Question 845006: One number is 4 times as large as another. The sum of their reciprocals is 35/4. Find the two numbers.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

One number is 4 times as large as another+highlight_green%28x%29. 

The sum of their reciprocals is 35/4.

+1%2F%284x%29+%2B+1%2Fx+=+35%2F4    |Multiplying thru by 4x so as all denominators = 1

   1 + 4 = 35x

   5 = 35x

   5/35 = x = 1/7

One number is 1/7 and the larger 4/7

CHECKING our answer***The sum of their reciprocals is 35/4.

  7/4 + 7 = 7/4 + 28/4 = 35/4

Wish You the Best in your Studies.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Numbers are x and 4x+
Sum of reciprocals is
1%2Fx+%2B+1%2F%284x%29+=+35%2F4+................solve for x
4+%2F4x%2B+1%2F%284x%29+=+35%2F4+
5%2F%284x%29+=+35%2F4+
5%2A4+=+35%2A4x+
5%2Across%284%29+=+35%2Across%284%29x+
5=+35x+
x+=+5%2F35+
highlight%28x+=+1%2F7%29 .....first number
4x+=4%281%2F7+%29
highlight%284x=4%2F7%29...........second number
their reciprocals:
reciprocal of 1%2F7 is 7 and reciprocal of 4%2F7 is 7%2F4
the sum of reciprocals should be 35%2F4
check it:
7%2B7%2F4=35%2F4
7%2A4%2F4%2B7%2F4=35%2F4
28%2F4%2B7%2F4=35%2F4
%2828%2B7%29%2F4=35%2F4
35%2F4=35%2F4 which confirms our solution is correct