One number is 4 times another. If the sum of their reciprocals is 5/36 , find the two numbers.
I am total lost on this problem
x is a number
4x is another number
these should = 5/36
so my equation would be
x+4x=5/36
first x i am getting 1/36
so the second would be 4/36=9
the two numbers be 1/36, 9
please explain to me what i have done wrong
the sum of their RECIPROCALS. which isn't x+4x
reciprocal of 5/36 is 36/5=7.2
does this mean my answers to add to
x =4x=7.2
please explain this to me
One number is 4 times another. If the sum of their reciprocals is 5/36 , find the two numbers.
x = 2y
1/x + 1/y = 5/36
You should be able to take it from here.
To solve this problem, let's start by assigning variables to the two numbers:
Let x be the smaller number.
Then 4x will represent the larger number, as given in the problem.
Now, we know that the sum of their reciprocals is equal to 5/36. So we can write the equation:
1/x + 1/(4x) = 5/36
To simplify this equation, we need to find a common denominator. In this case, the least common denominator is 4x. So we multiply each term by 4x:
4x * (1/x) + 4x * (1/(4x)) = 4x * (5/36)
Simplifying further:
4 + 1 = (20x)/36
Combining like terms on the left side:
5 = (20x)/36
To get rid of the fraction, we can cross-multiply:
5 * 36 = 20x
180 = 20x
Dividing both sides by 20:
x = 180/20
x = 9
Now that we have the value of x, we can find the larger number:
4x = 4 * 9 = 36
So the two numbers are 9 and 36.