Help problem below

Question

One number is four times a second number. If you take one-half of the second number and increase it by the first number, the result is at least 45. Find the least possible value for the second number

Answer 1

a = first number

b= second number

 

The first number is four times the second number:  a = 4b      (1)

 

One-half of the second number plus the first number is at least 45:    0.5b + a ≥ 45      (2)

 

Now, by plugging equation 1 into equation 2, we get:

 

0.5b + 4b ≥ 45

4.5b ≥ 45

b ≥ 45/4.5 = 10

 

The second number, b, must be at least 10.