Answer:
The answer is below
Step-by-step explanation:
Annie and Maria traveled overseas for 7 days and stayed in three different hotels in three different cities: Stockholm, Sweden; Oslo, Norway; and Paris, France.
The total bill for all seven nights (not including tax) was $1040. The total tax was $106. The nightly cost (excluding tax) to stay at the hotel in Paris was $80 more than the nightly cost (excluding tax) to stay in Oslo. Find the cost per night for each hotel excluding tax.
Solution:
Let x represent the cost per night to stay in Paris (France), let y represent the cost per night to stay in Stockholm (Sweden) and let z represent the cost per night to stay in Oslo (Norway).
They spent 1 night in Paris, 4 nights on Stockholm and 2 nights in Oslo, hence:
x + 4y + 2z = $1040 (1)
They were taxed 8% in Paris, 11% in Stockholm and 10% in Oslo, hence:
(8% of x) + (11% of 4y) + (10% of 2z) = $106
0.08x + 0.44y + 0.2z = 106 (2)
Also, The nightly cost (excluding tax) to stay at the hotel in Paris was $80 more than the nightly cost (excluding tax) to stay in Oslo. Hence:
x = z + 80
x - z = 80 (3)
Solving equations 1, 2 and 3 simultaneously gives:
x = $200, y = $150 and z = $120
Therefore they spent $200 per night in Paris, $150 per night in Stockholm and $120 per night in Oslo.
