If 2 is added to half of a number, the result is one more than the original number. What is the original number?
can I know how do you get the answer mam?
Suppose x is a number. The equation:
(1/2)x + 2 = x + 1
Solve, (note: (1/2)x is the same as x/2)
x/2 - x = 1 - 2
x/2 - x = -1
2*(x/2 - x) = -1 * 2
x - 2x = -2
-x = -2
x = 2
Verify:
If x = 2 then (1/2)x + 2 = x + 1
(1/2)(2) + 2 = 2 + 1
1 + 2 = 2 + 1
3 = 3 is true.
To find the original number, let's break down the information given in the problem.
We are given that "2 is added to half of a number". Let's represent the unknown number as 'x'. So, half of x would be (1/2)x, and if we add 2 to it, we get (1/2)x + 2.
The problem also states that this result is "one more than the original number". In other words, this expression (1/2)x + 2 should be equal to x + 1.
So, we can set up the equation: (1/2)x + 2 = x + 1.
To solve this equation, we can start by multiplying both sides by 2 to eliminate the fraction: 2((1/2)x + 2) = 2(x + 1).
This simplifies to x + 4 = 2x + 2.
Now, let's isolate the variable 'x' on one side of the equation. We can do this by subtracting x from both sides: x - x + 4 = 2x - x + 2.
Simplifying further, we get 4 = x + 2.
Finally, subtract 2 from both sides to solve for 'x': 4 - 2 = x + 2 - 2.
This gives us x = 2.
Therefore, the original number is 2.