SOLUTION: Before, solving the problem, I just want to give you the heads up. It's Application of Rational Equations. I can't find the specific title to relate with my story problems. My chap

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Question 190058: Before, solving the problem, I just want to give you the heads up. It's Application of Rational Equations. I can't find the specific title to relate with my story problems. My chapter in the book is Chapter Six Solving Rational Equations and Application of rational Equations. Hope it helps!
One number is 4 times as larger as another. The sum of their reciprocals is 5/12. Find the two numbers.
Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = "a number"
Let y = "another number
:
write an equation for each statement:
"One number is 4 times as larger as another."
x = 4y
:
" The sum of their reciprocals is 5/12."
1%2Fx + 1%2Fy = 5%2F12
:
From the 1st statement substitute 4y for x in the above equation:
1%2F%284y%29 + 1%2Fy = 5%2F12
Multiply equation by 12y; results
3 + 12 = 5y
5y = 15
y = 15%2F5
y = 3
:
Remember x = 4y
x = 4(3)
x = 12
:
Check solution in the 2nd statement
1%2F%2812%29 + 1%2F3 = 5%2F12
1%2F%2812%29 + 4%2F12 = 5%2F12



Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the first number and m be the second number.
1) n+=+4M "One number (n) is four time as large as another (m)"
2) 1%2Fn+%2B+1%2Fm+=+5%2F12 "The sum of their reciprocals is 5%2F12" Substitute n+=+4m into the second equation.
1%2F4m+%2B+1%2Fm+=+5%2F12 Add the fractions on the left side.
%285%29%2F4m+=+5%2F12 Solve for m.Multiply both sides by 4m.
5+=+4m%285%2F12%29 Multiply both sides by 12%2F5
5%2812%2F5%29+=+4m Divide both sides by 4.
12%2F4+=+m
m+=+3
n+=+4m
n+=+4%283%29
n+=+12
The two numbers are 3 and 12.