four times the sum of3 and a number yields the difference between 15 and 5 times the number
4(n+3) = 15-5n
4n - 12 = 15 - 5n
Combine like terms to solve.
Let's break down the problem step by step to find the solution.
Let's first assume that the number is represented by the variable "x".
According to the problem, "four times the sum of 3 and a number (4*(3+x)) yields the difference between 15 and 5 times the number (15 - 5x)."
Now we can set up an equation to solve for x:
4*(3+x) = 15 - 5x
To solve this equation, we can simplify both sides separately:
On the left side, distribute the 4:
12 + 4x = 15 - 5x
Now, we can combine like terms by moving all the terms with x to one side of the equation:
4x + 5x = 15 - 12
9x = 3
To isolate x, divide both sides of the equation by 9:
x = 3/9
Simplifying further, we get:
x = 1/3
So, the number is 1/3.