One-third a number (x)added to one-half the number equals twelve less than the number
Ah, I see we have a math problem here. Well, let's see if we can solve it with a touch of humor!
So, according to the question, one-third of a number (x) added to one-half of the number equals twelve less than the number... That's quite a mouthful, isn't it? It's like a math problem that's practicing its karate skills!
Now, let's break it down. One-third of a number is like saying, "Hey, I only want a small portion of that number!" And one-half of the number is like saying, "I'll take half, please!"
So, we have this equation: (1/3)x + (1/2)x = x - 12. It's like a math buffet!
To figure out this riddle, let's add those fractions together. (1/3) + (1/2) = (2/6) + (3/6) = (5/6). So, we have (5/6)x = x - 12. It's like trying to teach fractions to a bunch of rebellious numbers!
Now, we'll multiply both sides by 6 to get rid of that pesky fraction. 5x = 6(x - 12). It's like math playing hide and seek!
Expanding the equation gives us 5x = 6x - 72. Did x go on a vacation?
Now, let's bring all the x's to one side and the numbers to the other. We have 5x - 6x = -72. Math is like a magician trying to make things disappear!
Simplifying, we get -x = -72. Now, we'll multiply both sides by -1 to solve for x. That means x = 72. Voilà! We found our number! It's like finding a needle in a haystack made of numbers!
So, the answer is x = 72. And remember, math might be tricky, but with a dash of humor, we'll solve it like circus clowns juggling numbers!
To solve this problem step-by-step, we can translate the sentence into an equation:
One-third of a number (x) added to one-half of the number equals twelve less than the number.
Step 1: Translate the sentence into an equation.
(x/3) + (x/2) = x - 12
Step 2: Simplify the equation by finding a common denominator.
(2x + 3x) / 6 = x - 12
Step 3: Combine like terms on the left side of the equation.
5x / 6 = x - 12
Step 4: Multiply both sides of the equation by 6 to eliminate the fraction.
6 * (5x / 6) = 6 * (x - 12)
5x = 6x - 72
Step 5: Subtract 6x from both sides of the equation.
5x - 6x = 6x - 6x - 72
-x = -72
Step 6: Divide both sides of the equation by -1 to solve for x.
(-x) / (-1) = (-72) / (-1)
x = 72
Therefore, the number is 72.
To solve this problem, let's break it down step by step.
Step 1: Understand the problem.
We need to find the number (x) that satisfies the condition: One-third of the number plus one-half of the number equals twelve less than the number.
Step 2: Translate the problem into an equation.
Since the problem asks for a number (x), we can translate the condition into an equation:
1/3 * x + 1/2 * x = x - 12
Step 3: Simplify the equation.
To solve the equation, we need to simplify it by combining like terms:
(1/3 + 1/2) * x = x - 12
Step 4: Find a common denominator.
To add the fractions on the left side of the equation, we need a common denominator. The least common multiple (LCM) of 3 and 2 is 6, so we can rewrite the equation as:
(2/6 + 3/6) * x = x - 12
Step 5: Add the fractions.
Combining the fractions on the left side of the equation gives us:
(5/6) * x = x - 12
Step 6: Isolate the variable.
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by (5/6):
[(5/6) * x] / (5/6) = (x - 12) / (5/6)
This simplifies to:
x = (6/5) * (x - 12)
Step 7: Distribute the factor.
Distribute (6/5) to the terms inside the parentheses on the right side of the equation:
x = (6/5) * x - (6/5) * 12
Step 8: Simplify the equation.
Multiply (6/5) by x and (6/5) by 12:
x = (6/5) * x - (6/5) * 12
x = (6/5) * x - 72/5
Step 9: Move x to one side of the equation.
To isolate x, we can subtract (6/5) * x from both sides of the equation:
x - (6/5) * x = (6/5) * x - 72/5
(1 - 6/5) * x = -72/5
Step 10: Simplify the equation.
Combine the terms on the left side of the equation:
(5/5 - 6/5) * x = -72/5
(-1/5) * x = -72/5
Step 11: Solve for x.
To solve for x, we can multiply both sides of the equation by (-5/1) to cancel out the fraction on the left side:
(-1/5) * x * (-5/1) = -72/5 * (-5/1)
Multiplying gives us:
x = 360/5
Simplifying further:
x = 72
Therefore, the number is 72.
x/3 + x/2 = x-12
5/6 x = x-12
-1/6 x = -12
x = 72
check:
24+36 = 72-12
yep.