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

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!