a positive integer is 4 less than another.if the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/6,then find the two integers

Question

this is a math word problem.

Answer 1

answer deleted - I made an error!

Answer 2

For math word problems, break up the parts into manageable pieces. "A positive integer is 4 less than another"=> two integers such that a=b-4 (a is 4 less than b). (Note that these variable names are arbitrary and meaningless, just a symbol to represent the big and small integers). "If the sum of the reciprocal of the smaller..."=> You are adding the reciprocal of a to something (1/a +...). "... twice the reciprocal of the larger is 5/6"=> twice means multiply by 2, so 2*(1/b)=2/b. Add that to you equation: (1/a)+(2/b)=5/6. From here, you have two unknowns and two equations. 

a=b-4

(1/a)+(2/b)=5/6

It may be helpful to use this generalized formula: a/c+b/d=(ad+bc)/cd. Also note that solving this system of equations is going to result in using the quadratic formula. Remember that the answer must be an integer when dealing with the ±

Answer 3

Hi, Lashannon!

 

Ok, let's call the larger number X

 

So, the smaller number is X-4

 

1/(X-4) + 2(1/X) = 5/6

[x+2(x-4)]/x(x-4) = 5/6

 

if we cross multiply, we get:

6(x + 2x -8) = 5x² - 20x

5x² - 38x + 48 = 0

(x- 6)(5x - 8) = 0

x = 6, 8/5

 

Since 8/5  is not an integer, it is not the answer to this problem.

 

Therefore, X = 6  and X-4 = 2

 

So the integers are  2 and 6