Four times a number, increased by 25 is 13 less than 6 times the number. What is the number?
4n+25=-13-6n. ???
You're partly right.
4n + 25 = 6n - 13
25 + 13 = 6n - 4n
38 = 2n
19 = n
To solve this problem, we need to translate the given statement into an equation and then solve for the unknown variable, which in this case is the number.
The given statement is: "Four times a number, increased by 25 is 13 less than 6 times the number."
Let's break it down step by step:
"Four times a number" can be represented as 4n.
"Increased by 25" means we add 25 to it, so we have 4n + 25.
"Is 13 less than 6 times the number" can be written as 6n - 13.
Putting it all together, we get the equation:
4n + 25 = 6n - 13
To solve for n, we need to isolate the variable on one side of the equation. We can do this by moving the terms containing n to one side and the constant terms to the other side.
Let's start by subtracting 4n from both sides of the equation:
4n + 25 - 4n = 6n - 13 - 4n
25 = 2n - 13
Next, let's add 13 to both sides of the equation:
25 + 13 = 2n - 13 + 13
38 = 2n
Finally, to solve for n, we divide both sides of the equation by 2:
38/2 = 2n/2
19 = n
Therefore, the number is 19.