one number is two less than a second number. If you take one-half of the first number and increase it by the second number,the result is atleast 41. find the least possible value for the second number.
second number ---- x
first number ----- x-2
"If you take one-half of the first number and increase it by the second number,the result is atleast 41"
-----> (1/2)x + x-2 ≥ 41
solve for x to get your second number, then evaluate x-2 for the first.
It is up to you to decide if only whole numbers are allowed or if you include fractions.
Let's solve this step-by-step:
Let's assume the first number is x.
According to the statement, the first number is two less than the second number, so the second number would be x + 2.
Now, let's take one-half of the first number and increase it by the second number:
(1/2)x + (x + 2) = atleast 41
To find the least possible value for the second number, let's determine the smallest value for x that satisfies the equation.
Now, let's solve the equation:
(1/2)x + (x + 2) = 41
Simplify the equation:
(1/2)x + x + 2 = 41
Combine like terms:
(3/2)x + 2 = 41
Subtract 2 from both sides of the equation:
(3/2)x = 39
Multiply both sides of the equation by 2/3 to isolate x:
x = (2/3) * 39
x = 26
So the least possible value for the second number would be x + 2, which is:
26 + 2 = 28
Therefore, the least possible value for the second number is 28.
To find the least possible value for the second number, let's break down the problem step by step.
Let's assume the second number is x. Then, according to the problem, the first number is two less than x, which can be expressed as (x - 2).
Now, we need to find a condition related to the relationship between the two numbers. The problem states that if we take one-half of the first number ((1/2)*(x - 2)) and increase it by the second number (x), the result is at least 41. Mathematically, this can be written as:
(1/2)*(x - 2) + x ≥ 41
To solve this inequality, we can simplify the equation:
(1/2)*(x - 2) + x ≥ 41
(x/2 - 1) + x ≥ 41
x/2 + x - 1 ≥ 41
3x/2 ≥ 42
3x ≥ 84
x ≥ 28
Therefore, the least possible value for the second number is 28.