A collection of jewelry includes two rings, one 18 years old and the other 46 years old. In how many years will the older ring be twice as old as the newer ring?

In 10 years.

Step-by-step explanation:

1. 46-18=28

2. 28 (2)= 56

3. 56-46=10

(4. 18+10=28)

5. So, after 10 years, the older ring will be 56 years old and the younger ring will be 28 years old. 56 is twice as much as 28. (28+28=56, 28(2)=56 or 56/2=28)

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: