A certain number was increased 5 times, then decreased by 3, then halved. The result was 0.3 less than the original number. What was the original number?
To solve this problem, let's break it down step by step and create an equation to represent the given information.
Step 1: Let's assume the original number is represented by the variable "x".
Step 2: The number was increased 5 times, so we multiply it by 5: 5x
Step 3: The result was then decreased by 3: 5x - 3
Step 4: The new number was then halved: (5x - 3)/2
Step 5: According to the problem, this result is 0.3 less than the original number, so we subtract 0.3 from x: x - 0.3
Step 6: Now we can set up our equation by equating the two expressions for the number: (5x - 3)/2 = x - 0.3
To solve this equation, we can start by multiplying both sides of the equation by 2 to eliminate the fraction, which gives us: 5x - 3 = 2(x - 0.3)
Next, distribute the 2 on the right side of the equation: 5x - 3 = 2x - 0.6
Now, let's isolate the x terms by subtracting 2x from both sides of the equation: 5x - 2x - 3 = -0.6
Combine like terms: 3x - 3 = -0.6
Add 3 to both sides of the equation to isolate the x term: 3x - 3 + 3 = -0.6 + 3
Simplify: 3x = 2.4
Finally, divide both sides of the equation by 3 to solve for x: x = 2.4/3
The original number is x = 0.8. Therefore, the original number is 0.8.
"increased 5 times" could mean
x(+x) 5 times = 6x
or
x*5 = 5x
I'll assume the latter, but you can fix it if you need to
(5x+3)/2 = x - 0.3