One more than a number is the same as 5 times the number decreased by 15. What does this mean?
n + 1 = 5n - 15
n = 4
One number is equal to the product of -2 and the difference between another (n) and 5. The sum of the numbers is 16. What is the second number?
This means that if we let the unknown number be represented by x, then the equation can be written as "one more than a number" which is (x+1), is equal to "5 times the number" which is (5x), decreased by 15, which is (5x - 15).
So, the equation can be written as: (x+1) = (5x - 15).
This statement is a mathematical equation describing a relationship between "a number" and "one more than that number." Let's break it down step by step to understand its meaning.
We can represent "a number" as x. Adding "one more than that number" to x gives us x + 1.
The equation also states that "5 times the number decreased by 15" is equal to "one more than the number." Mathematically, this can be written as:
5x - 15 = x + 1
Now, we need to solve this equation to find the value of the number (x) that satisfies this relationship.
To solve it, we can start by isolating x on one side of the equation. Let's do that by subtracting x from both sides:
5x - x - 15 = x - x + 1
Simplifying this equation gives us:
4x - 15 = 1
Next, we can isolate 4x by adding 15 to both sides of the equation:
4x - 15 + 15 = 1 + 15
Simplifying further:
4x = 16
To find the value of x, we divide both sides of the equation by 4:
4x/4 = 16/4
Simplifying:
x = 4
So, the solution to the equation is x = 4. This means that the number we were referring to in the statement is 4.