I think of a number. If I divide the sum of 6 and the number by 3, the result is 4 more than one quarter of the number. Find the number.
(n+6)/3 = 4 + n/4
Now work your magic
Two times the summer three and a number
To find the number, let's break down the given information and work through it step by step.
Let's call the unknown number "x".
The problem states that the sum of 6 and the number x divided by 3 is equal to 4 more than one quarter of the number.
Translated into an equation, this can be written as:
(x + 6)/3 = (x/4) + 4
To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators (in this case, 12) to remove the fractions.
12 * [(x + 6)/3] = 12 * [(x/4) + 4]
Simplifying this expression gives:
4(x + 6) = 3(x/4) + 12
Now, distribute and combine like terms:
4x + 24 = 3x/4 + 12
Next, let's get rid of the fraction by multiplying through by 4:
4(4x + 24) = 3x + 48
Expand and simplify further:
16x + 96 = 3x + 48
Now, let's isolate the variable x by subtracting 3x from both sides:
16x - 3x + 96 = 3x - 3x + 48
13x + 96 = 48
To further isolate x, subtract 96 from both sides:
13x + 96 - 96 = 48 - 96
13x = -48
Finally, divide both sides by 13:
(13x)/13 = -48/13
x = -48/13
Thus, the number is -48/13.