Avg of two terms & largest possible value

[zak100]

Homework Statement

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

Homework Equations

Avg of two variables is:
(a+b)/2

The Attempt at a Solution

(3a + 4b)/2 < 50
3a + 4b <100
Now try out values such a = 2b
I) a= 10 & b=20
3(10) + 4(20) <100
30 + 80 <100
110<100 false
2) a=9 & b = 18
3(9) + 4(18)
27 + 72
99
but this answer is not correct. Some body please guide me.
Zulfi.

 

[Filip Larsen]

You seem to have flipped the meaning of a and b when you chose numbers.

 

[Ray Vickson]

Homework Statement

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

Homework Equations

Avg of two variables is:
(a+b)/2

The Attempt at a Solution

(3a + 4b)/2 < 50
3a + 4b <100
Now try out values such a = 2b
I) a= 10 & b=20
3(10) + 4(20) <100
30 + 80 <100
110<100 false
2) a=9 & b = 18
3(9) + 4(18)
27 + 72
99
but this answer is not correct. Some body please guide me.
Zulfi.

If you know that a = 2b, why do you not just express everything in terms of b alone?

 

[zak100]

Hi,
<You seem to have flipped the meaning of a and b when you chose numbers.>

Reference https://www.physicsforums.com/threads/avg-of-two-terms-largest-possible-value.895671/
Thanks. This means that 'a' should be less than 20 i.e a =19.
Zulfi.

 

[haruspex]

i.e a =19

Yes, unless b is also supposed to be an integer. I agree it does not say so.