Two consecutive even whole numbers are selected. The difference between the reciprocals of the two numbers is 1/60. Determine the numbers.
look at this question from 2007
www.jiskha.com/questions/49548/Find-two-consecutive-numbers-such-that-the-difference-of-their-reciprocals-is-1-4
Yours just has different constants
let the first even number be x
the the next even number is x+2
1/x - 1/(x+2) = 1/60
you will end up with a quadratic, remember you answer must be a positive whole number.
Let's represent the first even number as x, and the second consecutive even number as x+2.
According to the given information, the difference between the reciprocals of the two numbers is 1/60.
So, we can set up the equation as:
1/x - 1/(x+2) = 1/60
To solve the equation, we'll first find a common denominator by multiplying both sides by 60x(x+2).
60(x+2) - 60x = x(x+2)
Now, let's simplify the equation:
60x + 120 - 60x = x^2 + 2x
120 = x^2 + 2x
Rearranging the equation:
x^2 + 2x - 120 = 0
Now, we'll factorize the equation:
(x + 12)(x - 10) = 0
We have two possible solutions:
x + 12 = 0 or x - 10 = 0
x = -12 or x = 10
Since we are looking for even whole numbers, we can disregard the negative solution.
Therefore, the first even number (x) is 10 and the second even number (x+2) is 12.
Hence, the two numbers are 10 and 12.
To solve this problem, let's assign variables to the two consecutive even whole numbers. Let's call the first number "x," and since the numbers are consecutive even whole numbers, the second number will be "x + 2" (because the next even number after x is x + 2).
Now, we can form an equation using the information given. The difference between the reciprocals of the two numbers is 1/60. Mathematically, this can be written as:
1/x - 1/(x + 2) = 1/60
To further simplify the equation, we can multiply each term by the least common denominator, which is 60x(x+2):
60(x+2) - 60x = x(x+2)
Expanding both sides of the equation:
60x + 120 - 60x = x^2 + 2x
Simplifying further:
120 = x^2 + 2x
Rearranging the equation to set it equal to zero:
x^2 + 2x - 120 = 0
Now, to solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, the equation factors nicely:
(x + 12)(x - 10) = 0
Setting each factor equal to zero:
x + 12 = 0 or x - 10 = 0
Solving for x in each equation:
x = -12 or x = 10
Since the numbers need to be even, we disregard the negative value (-12) and conclude that the first number, x, is 10. Therefore, the two consecutive even whole numbers are 10 and 12.