What is a equation for this problem?

Question

The sum of a number, half of that number, and 5 is at least 35.

Answer 1

 

 X + X/2 + 5 >= 35

 

(1)X + (1/2)X + 5 >= 35

 

(2/2)X + (1/2)X + 5 >= 35

 

(3/2)X + 5 >= 35

 

(3/2)X >= 30

 

X >= 30 ( 2/3) = 10*2 = 20

 

check: let x=20  

 

       20+ 1/2*20+ 5 = 20 + 10 + 5 = 35 >= 35 <--- YES, it works

 

      let x = 30

     30 + 1/2(30) + 5 = 30 +15 +5 = 50 >= 35 <---, YES, it works !!!!

 

    let x = 15

      15 + 1/2(15) +5 = 15+ 15/2 + 5 = 20 + 15/2 = 27 and 1/2 >= 35 is FALSE<-- fails as expected

     

Answer 2

Let two numbers be x and 2x.  By logic, one of these numbers is half the other, and one is twice the other.

 

x is half of 2x.

 

 

Then your inequality is     x + 2x + 5 ≥ 35

 

                                       3x + 5 ≥ 35