A number is added to 6. The sum is then multiplied by 6. Then, 6 is again subtracted from the product. When the difference divided by 6, the result is still 6. What is this number?
Let's call the number we are trying to find "x".
The first step is to add x to 6, which gives us 6 + x.
Next, we multiply the sum by 6, so we have 6(6 + x) = 36 + 6x.
Then, we subtract 6 from the product, giving us 36 + 6x - 6 = 30 + 6x.
Finally, we divide the difference by 6, so (30 + 6x) / 6 = 6.
Simplifying the equation, we get 30 + 6x = 36.
Subtracting 30 from both sides, we have 6x = 6.
Dividing both sides by 6, we find that x = 1.
Therefore, the number we are looking for is 1.
Let's denote the unknown number as "x".
1) A number is added to 6:
6 + x
2) The sum is then multiplied by 6:
6 * (6 + x)
3) 6 is subtracted from the product:
(6 * (6 + x)) - 6
4) When the difference divided by 6, the result is still 6:
((6 * (6 + x)) - 6) / 6 = 6
To find the value of x, we can solve the equation:
((6 * (6 + x)) - 6) / 6 = 6
Simplifying, we have:
(6 * (6 + x)) - 6 = 36
Distributing,
36 + 6x - 6 = 36
Simplifying further,
6x = 36
Dividing both sides of the equation by 6,
6x/6 = 36/6
x = 6
Hence, the number is 6.
To solve this problem, let's break it down step by step.
1. A number is added to 6: Let's call this number "x". The sum of the number and 6 is x + 6.
2. The sum is then multiplied by 6: We multiply the sum (x + 6) by 6, which gives us 6(x + 6).
3. 6 is subtracted from the product: We subtract 6 from the result of step 2, which gives us 6(x + 6) - 6.
4. The difference is divided by 6: Finally, we divide the result of step 3 by 6, which gives us (6(x + 6) - 6) / 6.
According to the problem, the result of this division is still 6. So, we can set up the equation:
(6(x + 6) - 6) / 6 = 6
Now, let's solve this equation to find the value of "x".
First, simplify the equation:
6(x + 6) - 6 = 6 * 6
Distribute 6 to the terms inside the parentheses:
6x + 36 - 6 = 36
Combine like terms:
6x + 30 = 36
Subtract 30 from both sides of the equation:
6x = 6
Divide both sides of the equation by 6:
x = 1
Therefore, the number is 1.