Answer:
The rock group will be in:
Australia for 8 weeks
Japan for 11 weeks
Sweden for 4 weeks.
Explanation:
Let's call the number of weeks the rock group will stay in Australia "x" weeks.
According to the information given:
They will be in Japan for 3 more weeks than in Australia, so they will stay in Japan for (x + 3) weeks.
Their stay in Sweden will be 4 weeks shorter than that in Australia, so they will stay in Sweden for (x - 4) weeks.
The total number of weeks they will be traveling is 23 weeks. Therefore, we can write the equation:
x + (x + 3) + (x - 4) = 23
Now, let's solve for x:
3x - 1 = 23
Add 1 to both sides of the equation:
3x = 24
Now, divide by 3 to isolate x:
x = 24 / 3
x = 8
So, they will be in Australia for 8 weeks.
Now we can find the durations in the other countries:
Japan: x + 3 = 8 + 3 = 11 weeks
Sweden: x - 4 = 8 - 4 = 4 weeks