If one-fourth of the sum of a number and seven is four less than three times the number, find the number.
Why did the number go to therapy?
Because it couldn't figure out its identity crisis!
But to solve this perplexing problem, let's break it down step by step.
Let's call the number "x".
According to the problem, one-fourth of the sum of the number and seven is four less than three times the number. In equation form, this can be written as:
(1/4)(x + 7) = 3x - 4
To find x, let's solve for it. Brace yourself, numbers!
First, let's get rid of the fraction by multiplying both sides of the equation by 4:
4 * (1/4)(x + 7) = 4 * (3x - 4)
Simplifying, we get:
x + 7 = 12x - 16
Now let's get our x's all together by subtracting x from both sides:
7 = 11x - 16
Adding 16 to both sides:
23 = 11x
And finally, divide both sides by 11:
x = 23/11
So, after all that calculation, the number is approximately 2.09.
Remember, math may seem intimidating, but with a dash of humor, it becomes a bit more enjoyable!
Let's break down the problem step-by-step:
Step 1: Let's assume the number we're trying to find is represented by the variable "x".
Step 2: The sum of a number and seven can be written as "x + 7".
Step 3: One-fourth of the sum of a number and seven is (1/4) * (x + 7).
Step 4: Three times the number can be written as "3x".
Step 5: Four less than three times the number is "3x - 4".
Step 6: According to the problem, the expression "(1/4) * (x + 7)" is equal to "3x - 4".
Step 7: Now, we can set up the equation:
(1/4) * (x + 7) = 3x - 4
Step 8: Let's solve the equation:
Multiply both sides of the equation by 4 to eliminate the fraction:
4 * (1/4) * (x + 7) = 4 * (3x - 4)
(x + 7) = 12x - 16
Step 9: Simplify the equation:
x + 7 = 12x - 16
Subtract x from both sides:
7 = 11x - 16
Step 10: Add 16 to both sides:
7 + 16 = 11x - 16 + 16
23 = 11x
Step 11: Divide both sides by 11:
23/11 = 11x/11
x = 2
So, the number we were trying to find 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".
One-fourth of the sum of the number and seven can be expressed as (1/4)(x + 7).
Four less than three times the number can be expressed as 3x - 4.
According to the information given, the equation becomes:
(1/4)(x + 7) = 3x - 4
To solve this equation, we can start by eliminating the fraction by multiplying both sides of the equation by 4:
4 * (1/4)(x + 7) = 4 * (3x - 4)
This simplifies to:
x + 7 = 12x - 16
Next, let's isolate the variable terms on one side by subtracting x from both sides and adding 16 to both sides:
x - 12x = -16 - 7
Combining like terms, we have:
-11x = -23
Finally, divide both sides of the equation by -11 to solve for x:
x = (-23) / (-11)
Simplifying the expression further, we get:
x ≈ 2.0909
Therefore, the number is approximately 2.0909.
Translate into English.
"One-fourth of the sum of a number and seven is four less than three times the number."
If the number is x
(1/4)x + 7 = 3x - 4
x/4 - 3x = -11
times 4
x - 12x = -44
-11x = -44
x = 4