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A rock group plans to travel for a total of 35 weeks, making three concert stops. They will be in Japan for 3 more weeks than they will be in Australia. Their stay in Sweden will be 4 weeks shorter than that in Australia. How many weeks will they be in each country?

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"
translates to
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.

Namely:
35 = (A + 3) + A + (A -4)
simplifying gives
35 = 3*A - 1