Question

Real world compositionsShoe sizes are marked differently in many countries. In Japan, a shoe size is 16 more than the size in the United States. In Korea, a shoe size is 224 more than the size in Japan. Determine the function of the U.S. size of a shoe in terms of the shoe size in Korea. What is the U.S. shoe size of a shoe that is 250 in Korea? Solve using composite functions

Answer 1

To solve this exercise, we define the following variables:

• j = Japan size of shoes,

,

• u = United Sates size of shoes,

,

• k = Korea size of shoes.

From the statement of the problem, we know that:

0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,

,

1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.

We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).

1) From point 1, we have:

`\begin{gathered} j=16+u, \\ u=j-16. \end{gathered}`

2) From point 2, we have:

`\begin{gathered} k=224+j, \\ j=k-224. \end{gathered}`

Replacing the expression of j in terms of k in the expression of u, we get:

`u=j-16=(k-224)-16=k-240.`

Replacing the value k = 250 in the last equation, we get:

`u=250-240=10.`

Answer

The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.