If 16 is added to one-third of a number, the result is three times the number. What is the number?
(1/3)x + 16 = 3x
multiply each term by 3
x + 48 = 9x
carry on
Let's solve this step-by-step:
Step 1: Let's assume the number we are looking for is "x".
Step 2: We are given that "16 is added to one-third of x".
Step 3: According to the question, this sum is equal to three times the number x.
Step 4: Putting this information into an equation, we get the equation: (1/3)x + 16 = 3x.
Step 5: To solve the equation, let's simplify it first.
Multiplying the equation by 3 to get rid of the fraction, we have: 3 * ((1/3)x + 16) = 3 * 3x.
Simplifying further, we get: x + 48 = 9x.
Step 6: Now, let's isolate x by subtracting x from both sides of the equation.
Subtracting x from both sides, we have: x + 48 - x = 9x - x.
Simplifying, we get: 48 = 8x.
Step 7: To isolate x, divide both sides of the equation by 8.
Dividing both sides by 8, we have: 48/8 = 8x/8.
Simplifying, we get: 6 = x.
Therefore, the number we were looking for is 6.
To find the number, let's break down the given information and create an equation to solve for it.
Let's assume the number is represented by the variable x.
According to the problem, "16 is added to one-third of the number." This can be translated into an equation as:
1/3 * x + 16
The problem also states that "the result is three times the number." This can be translated into an equation as:
3 * x
Combining both equations, we get:
1/3 * x + 16 = 3 * x
To solve this equation, we need to isolate the variable x on one side.
First, we can multiply both sides of the equation by 3 to eliminate the fraction:
3 * (1/3 * x + 16) = 3 * (3 * x)
x + 48 = 9 * x
Next, we can subtract x from both sides to gather the variable terms on one side:
x + 48 - x = 9 * x - x
48 = 8 * x
Then, divide both sides of the equation by 8 to solve for x:
48 / 8 = 8 * x / 8
6 = x
Therefore, the number is 6.