Iwrote down 3 different positive whole numbers that add 96. the sum of any 2 is divisible by the third.

what is the largest of these numbers?

This question is really simple if you focus on this part

“The sum of any two is divisible by the third”

⟹⟹ Pairwise, the numbers must have a GCD greater than one.

Let this GCD be xx.

The first three easiest numbers I can think of are x,2xx,2x and 3x3x

Because

gcd(x,2x)=gcd(2x,3x)=gcd(3x,x)=xgcd(x,2x)=gcd(2x,3x)=gcd(3x,x)=x

The numbers sum to 9696

⟹x+2x+3x=96⟹x+2x+3x=96

⟹6x=96⟹6x=96

⟹x=16⟹x=16

The largest number is 3x=3×16=483x=3×16=48

Thanks for the A2A

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

312312

step-by-step explanation: