Question

an advertising agent goes on a vacation to three countries, India, New Zealand and Australia. he spends three times the number of days in New zealand than he does in Australia and five days longer in India then in Australia. If his total vacation duration is 40 days, how many day did he spend in Australia?

Answer 1

Let i, n, a be the number of days in India, New Zealand and Australia respectively. Then, from the given conditions we can construct the system of equations:

$\begin{cases} n = 3a; \\ i = a+5; \\ i + n + a = 40; \\ \end{cases}$

Now solving for a, we will substitute the values for $n, i$ from the first and the second equations into the the third equation:

$3a+a+5+a = 40;\\ 5a = 40-5 ; \\ 5a=35; \\ a = 7.$

Answer: 7 days in Australia.