21 is three times the difference between 4 times a number and 5.
21 = 3(4n - 5)
Solve for n.
To find the number, let's break down the problem step by step.
Let's assume the number is represented by "x".
Step 1: "Four times a number"
Four times a number can be represented as 4 * x or 4x.
Step 2: "Difference between 4 times a number and 5"
The difference between 4 times a number and 5 can be represented as 4x - 5.
Step 3: "Three times the difference between 4 times a number and 5"
Three times the difference between 4 times a number and 5 can be represented as 3(4x - 5).
According to the problem, 21 is three times the difference between 4 times a number and 5.
Step 4: Setting up the equation:
3(4x - 5) = 21
Step 5: Solving the equation:
12x - 15 = 21
12x = 21 + 15
12x = 36
x = 36/12
x = 3
Therefore, the number is 3.
To solve this problem, we can use algebraic equations. Let's break down the given information into equations:
Let's represent the unknown number as "x".
- "Three times the difference between 4 times a number and 5" can be expressed as 3(4x - 5).
- "21 is three times the difference between 4 times a number and 5" can be written as 3(4x - 5) = 21.
Now we can solve for "x" using this equation:
3(4x - 5) = 21
First, distribute the 3 to the terms inside the parentheses:
12x - 15 = 21
Next, isolate the x term by moving the constant term (-15) to the right side:
12x = 21 + 15
12x = 36
Finally, divide both sides of the equation by 12 to solve for x:
x = 36/12
x = 3
Therefore, the unknown number is 3.