Three times the reciprocal of a number equals 9 times the reciprocal of 6. Find the number.
let the number be x
3(1/x) = 9(1/6)
3/x = 3/2
3x = 6
x = 2
check:
3(1/2) = 3/2
9(1/6) = 3/2 , looks good.
Well, this question reminds me of a math joke! Why did the number 6 hate the number 7? Because 7 8 (ate) 9! But let's get back to the question at hand.
To solve this problem, we can set up an equation. Let's call the number we're looking for "x". According to the problem, three times the reciprocal of x is equal to 9 times the reciprocal of 6.
So, we can write the equation as follows:
3 * (1/x) = 9 * (1/6)
Now, let's simplify this equation:
3/x = 9/6
Cross-multiplying, we get:
3 * 6 = 9 * x
18 = 9x
Dividing both sides by 9, we find:
x = 2
So, the number we're looking for is 2. And just like 7, it's perfectly safe from being eaten by any other numbers!
Let's assign a variable to the unknown number. Let's call it "x".
According to the given information, "Three times the reciprocal of a number equals 9 times the reciprocal of 6."
We can translate this sentence into an equation as follows:
3 * (1/x) = 9 * (1/6)
To solve this equation, we'll first simplify the right side by finding the reciprocal of 6:
3 * (1/x) = 9 * (1/6)
3 * (1/x) = 9/6
3 * (1/x) = 3/2
Now we have:
3/x = 3/2
To solve for x, we can cross multiply:
2 * 3 = 3 * x
6 = 3x
Finally, divide both sides of the equation by 3:
x = 6/3
x = 2
Therefore, the number is 2.
To find the number, let's first set up the equation based on the given information.
Let's assume the number is represented by the variable 'x'.
Three times the reciprocal of a number can be written as 3(1/x), and it equals 9 times the reciprocal of 6, which can be written as 9(1/6).
So, our equation becomes:
3(1/x) = 9(1/6)
To solve for 'x', we need to get rid of the fractions. We can do this by multiplying both sides of the equation by the common denominator, which, in this case, is 6x (the product of 6 and x).
6x * 3(1/x) = 6x * 9(1/6)
Simplifying, we have:
18 = 9x
Now, let's solve for 'x' by dividing both sides of the equation by 9:
18/9 = 9x/9
2 = x
Therefore, the number is 2.