The hardest part of problems like this is writing them out as a set of equations.
Let J = # weeks in Japan, A = # weeks in Australia, and S = # weeks in Sweden.
"a total of 35 weeks, making three concert stops"
35 = J + A + S
"Japan for 3 more weeks than they will be in Australia"
J = A + 3
"Sweden will be 4 weeks shorter than that in Australia"
S = A - 4
"How many weeks will they be in each country?"
means find the value of J, A, and S individually.
The nice thing is that you have 3 unknowns (J, A, and S) and 3 equations, so there is a solution.
The simplest approach here is to notice that J and S are both defined in relation to A. That means you can substitute the second and third equations into the first, solve for "A", then substitute A into the other equations.
35 = (A + 3) + A + (A -4)
35 = 3*A - 1
add (+1) to both sides
36 = 3*A
divide (3) from both sides
12 = A
so, 12 weeks in Australia.
J = A + 3 = (12) + 3 = 15 weeks
S = A - 4 = (12) - 4 = 8 weeks
Let's double check that 12 + 15 + 8 = 35...yup! Done!