the ratio of ten more than three times a number to the square of the same number is equal to one. what is the number?
(3x + 10) : x^2 = 1
(3x+10)/x^2 = 1
x^2 = 3x+10
x^2 - 3x - 10 = 0
(x - 5)(x + 2) = 0
x=5 or x = -2
Why did the number go to the therapist?
Because it had a complex identity crisis! (Get it? Ratio, square, number... it's all just adding to the confusion!)
But fear not, dear human, for I shall solve this riddle for you. Let's break it down step by step:
Let's assume the number is "x."
According to the problem, the ratio of ten more than three times the number "x" to the square of "x" is equal to one.
In equation form, that would be: (3x + 10) / x^2 = 1.
Now, let's solve for "x":
3x + 10 = x^2.
Rearranging, we have: x^2 - 3x - 10 = 0.
Factoring, we find: (x - 5)(x + 2) = 0.
So, the possible solutions are x = 5 or x = -2.
Voila! The number could be either 5 or -2. But remember, my dear friend, humor is the best solution in life.
Let's represent the number as "x".
According to the given information, the ratio of ten more than three times the number to the square of the same number is equal to one.
So, we can write it as an equation:
(3x + 10) / (x^2) = 1
To solve this equation, we can cross-multiply:
3x + 10 = x^2
Rearranging the equation in standard form:
x^2 - 3x - 10 = 0
Factoring the equation:
(x - 5)(x + 2) = 0
Setting each factor equal to zero:
x - 5 = 0 or x + 2 = 0
Solving for x:
x = 5 or x = -2
Therefore, the two possible solutions for x are 5 and -2.
To solve this problem, let's break it down step by step.
Step 1: Let's assume the number is represented by 'x'.
Step 2: Translate the given information into an equation. The ratio of ten more than three times a number (3x + 10) to the square of the same number (x^2) is equal to one.
Step 3: Write the equation using the information from Step 2:
(3x + 10) / x^2 = 1
Step 4: Simplify the equation by removing the denominator by multiplying both sides of the equation by x^2:
3x + 10 = x^2
Step 5: Rearrange the equation to set it equal to zero:
x^2 - 3x - 10 = 0
Step 6: Factor the quadratic equation (if possible) or use the quadratic formula to find the values of x.
In this case, we can factor the equation:
(x - 5)(x + 2) = 0
Step 7: Set each factor equal to zero and solve for x:
x - 5 = 0 or x + 2 = 0
Solving for x in each case gives us two possible values:
x = 5 or x = -2
So, the number could be either 5 or -2.