SOLUTION: one number is 3 times another number. Find the numbers if the sum of their reciprocal is 1.

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Question 511628: one number is 3 times another number. Find the numbers if the sum of their reciprocal is 1.
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2Fy+=+1
.
x+=+3y
.
1%2F%283y%29+%2B+1%2Fy+=+1
.
Multiply through by 3y
.
1+%2B+3+=+3y
.
3y+=+4
.
y+=+4%2F3
.
x+=+3%2A%284%2F3%29+=+3%2A4%2F3+=+4
.
Check the sum of reciprocals.
.
1%2F4+%2B+3%2F4+=+1
Correct.
.
Answer: One number is 4/3 and the other is 4.
.
Done.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+a+=+3b+
+1%2Fa+%2B+1%2Fb+=+1+
+1%2F%283b%29+%2B+1%2Fb+=+1+
Multiply both sides by +3b+
+1+%2B+3+=+3b+
+3b+=+4+
+b+=+4%2F3+
and,
+a+=+3b+
+a+=+4+
The numbers are 4/3 and 4
check:
+1%2Fa+%2B+1%2Fb+=+1+
+1%2F4+%2B+1%2F%284%2F3%29+=+1+
+1%2F4+%2B+3%2F4+=+1+
OK