Price of a single item

Question

I have this mathematical problem, and I don't know how to tackle it.

Total price of a jacket and shoes is $106$ euros.

The shoes cost $13$ more euros than the jacket.

How much does the jacket cost?

$S+J=106$

$S=J+13$

$J=?$

Is the question missing something?

With this question, can't the price of the jacket can be anything, or am I mistaken?

Answer 1

You want to solve the system $$j+s=106,\,s=j+13$$ for $j,$ with the variables standing for the obvious quantities.

This is a linear system of the form $x+y=a,\,x-y=b.$ This always has a unique solution.

Answer 2

$$S+J=106\tag1$$

$$S-J=13\tag2$$

subtract $(2)$ from $(1)$:

$$2J=106-13$$

Now can you determine the price of the jacket?

Answer 3

No, the question isn't missing anything. You can set it up as the equation 106 = (13 + x) + x, where x is the price of the jacket and (13 + x) is the price of the shoe.