When 3 is subtracted from a certain number and the result multiple by 5 the result is the same as when 3 is added to twice the number find the number
Let's use algebra to solve the problem.
Let the number be represented by "x".
According to the problem, when 3 is subtracted from the number and the result is multiplied by 5, we have:
5(x - 3)
And, when 3 is added to twice the number, we have:
2x + 3
We can set up an equation using these two expressions:
5(x - 3) = 2x + 3
Now, let's solve for x.
Expanding the left side of the equation:
5x - 15 = 2x + 3
Bringing the x terms to one side of the equation and the constant terms to the other side:
5x - 2x = 3 + 15
3x = 18
Dividing both sides of the equation by 3:
x = 6
Therefore, the number is 6.
Let's solve the problem step-by-step:
Let's assume the certain number as 'x'.
Step 1: "When 3 is subtracted from a certain number"
When 3 is subtracted from 'x', the result is 'x - 3'.
Step 2: "The result multiplied by 5"
If we multiply the result 'x - 3' by 5, we get '5(x - 3)'.
Step 3: "The result is the same as when 3 is added to twice the number"
When 3 is added to twice the number 'x', we get '2x + 3'.
Step 4: To find the number:
Setting up the equation: 5(x - 3) = 2x + 3.
Step 5: Solving the equation:
5x - 15 = 2x + 3.
Subtracting 2x from both sides: 5x - 2x - 15 = 3.
Combining like terms: 3x - 15 = 3.
Adding 15 to both sides: 3x - 15 + 15 = 3 + 15.
Combining like terms: 3x = 18.
Dividing both sides by 3: (3x) / 3 = 18 / 3.
Simplifying: x = 6.
Therefore, the number is 6.
To solve this problem, we'll set up an equation. Let's use the variable "x" to represent the unknown number.
First, we'll translate the given information into mathematical expressions.
"3 is subtracted from a certain number" can be written as x - 3.
"The result multiplied by 5" can be written as 5 * (x - 3).
"The result is the same as when 3 is added to twice the number" can be written as 3 + 2x.
Now we can set up the equation:
5 * (x - 3) = 3 + 2x
To solve this equation, we'll start by simplifying both sides:
5x - 15 = 3 + 2x
Next, we'll move all the terms involving x to one side of the equation:
5x - 2x = 3 + 15
Simplifying further:
3x = 18
Then, divide both sides of the equation by 3 to solve for x:
x = 6
Therefore, the number we're looking for is 6.