Question 89874
One number is 3 times another number.The sum of their reciprocals is 4/9.What are the numbers?The choices are 1 and 2,2 and 6, and 3 and 9.
:
Givens:
Let "another number" be: x, its reciprocal is: 1/x
Then "one number" is: 3x, its reciprocal is: 1/3x
sum means add
Problem to solve:
{{{1/x+1/3x=4/9}}}  Multiply both sides by the LCD, 9x:
{{{9x(1/x+1/3x)=9x(4/9)}}}
{{{9x/x+9x/3x=36x/9}}}
{{{9+3=4x}}}
{{{12=4x}}}
{{{12/4=4x/4}}}
{{{3=x}}}
"another number" x=3
"one number" 3x=3(3)=9
The numbers are 3 and 9.
Happy Calculating!!!