SOLUTION: If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest integer of a?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest integer of a?      Log On


   

Question 975957: If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest integer of a?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest integer of a?
:
%283a%2B4b%29%2F2 < 50
multiply both sides by 2
3a + 4b < 100
:
"a is twice b"
a = 2b
or
b = .5a
:
3a + 4b < 100
replace b with .5a
3a + 4(.5a) < 100
3a + 2a < 100
5a < 100
a < 100/5
a < 20
then a = 19 is the largest integer
:
:
Check this, find b, find the average
b = .5(19)
b = 9.5
3%2819%2B4%289.5%29%29+%2F2 = 47.5 is the mean