SOLUTION: 2. One number exceeds another by 5. The sum of their reciprocals equal to 19 divided by the product of the two numbers. Find the two numbers. (a) How will you set up t

Algebra ->  Graphs -> SOLUTION: 2. One number exceeds another by 5. The sum of their reciprocals equal to 19 divided by the product of the two numbers. Find the two numbers. (a) How will you set up t      Log On


   

Question 140018: 2. One number exceeds another by 5. The sum of their reciprocals equal to 19
divided by the product of the two numbers. Find the two numbers.
(a) How will you set up the problem?
(b) What is the equation that the one number exceeds another by 5?
(c) What is the product of two numbers, in terms of x?
(d) What is x? Also check your answer.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Let x=first number and y=second number
b)
Since "One number exceeds another by 5", this means that the first equation is y=x%2B5
c)
The product of the two numbers in terms of x is
x%28x%2B5%29=x%5E2%2B5x

d)
The value of x is 7


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So let's solve the problem


Let x=first number and y=second number

Since "One number exceeds another by 5", this means that the first equation is y=x%2B5

Also, because "The sum of their reciprocals equal to 19 divided by the product of the two numbers" we have the second equation

1%2Fx%2B1%2Fy=19%2F%28x%2Ay%29

1%2Fx%2B1%2F%28x%2B5%29=19%2F%28x%2A%28x%2B5%29%29 Plug in y=x%2B5


Multiply both sides by the LCD x%2A%28x%2B5%29 to clear out the fractions


x%2B5%2Bx=19 Distribute and multiply


2x%2B5=19 Combine like terms on the left side


2x=19-5Subtract 5 from both sides


2x=14 Combine like terms on the right side


x=%2814%29%2F%282%29 Divide both sides by 2 to isolate x


x=7 Divide

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Answer:
So our answer is x=7