# Avg of two terms & largest possible value

• zak100
In summary, the conversation discusses finding the largest possible integer value of a, given that the average of 3a and 4b is less than 50 and a is twice b. The attempt at a solution involves setting up an inequality and testing different values for a and b, leading to the conclusion that a should be less than 20.
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
Zulfi.

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

zak100 said:

## 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
Zulfi.

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

zak100 said:
i.e a =19
Yes, unless b is also supposed to be an integer. I agree it does not say so.

## What is the average of two terms?

The average of two terms is the sum of the two terms divided by 2. It is also known as the arithmetic mean.

## How do you find the average of two terms?

To find the average of two terms, add the two terms together and divide the sum by 2. This will give you the average of the two terms.

## What is the largest possible value of two terms?

The largest possible value of two terms depends on the numbers being used. If the two terms are positive, the largest possible value would be when both terms are equal. If the two terms are negative, the largest possible value would be when one term is close to 0 and the other is a large negative number.

## Can the average of two terms be a negative number?

Yes, the average of two terms can be a negative number if one term is positive and the other is negative. The negative average indicates that the terms are on opposite sides of 0.

## How is the average of two terms useful in mathematics and science?

The average of two terms is useful in mathematics and science as it allows us to find the middle point between two values. This can be helpful in calculating trends, making predictions, and determining the central tendency of a data set.

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