The average of three values is 50. First value is 1/2 of the third value. Third value is 30 more than second value. What is the first value?

Correct option is A

Given:
Average of three values = 50
First value = Half of the third value
Third value = Second value + 30
Formula Used:
Sum of values = Average × Number of values
Solution:
Let the third value be represented by a variable x.
The first value is half of the third value = $$\frac{x}{2}$$​​
The second value is 30 less than the third value = x - 30
Calculate the total sum of the three values = 50 × 3 = 150
Set up the equation for the sum of the terms:
$$\frac{x}{2}$$​ + (x - 30) + x = 150

$$\frac{5x}{2}$$​ - 30 = 150

$$\frac{5x}{2}$$​ = 180

x = $$\frac{180 × 2}{5}$$​​
x = 72
The third value is 72. Now calculate the first value:
$$\frac{72}{2}$$​ = 36
Final Answer
So the correct answer is (a)