SOLUTION: I need help learning how to solve this word problem. I'm not sure how to start. A natural number is 4 more than another natural number. When the reciprocal of the greater number is

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Question 728392: I need help learning how to solve this word problem. I'm not sure how to start. A natural number is 4 more than another natural number. When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is . What are the two numbers?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A natural number is 4 more than another natural number.
When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is . What are the two numbers?
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You did not give us the difference, so am going to give you a method
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Let a and b = the two numbers, let a be the greater number
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Write an equation for each statement:
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"A natural number is 4 more than another natural number."
a = b + 4
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" When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is ."
- = ?
multiply both sides by ab
b - a = ?ab
Add a to both sides
b = ?ab + a
factor out a
b = a(?b + 1)
Replace a with (b+4), from the 1st statement
b = (b+4)(?b+1)
FOIL this, develop a quadratic equation, find b
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Let me know how you do with this. CK