Annie and Maria traveled overseas for days and stayed in three different hotels in three different cities: Stockholm, Sweden; Oslo, Norway; and Paris, France. The total bill for all nights (not including tax) was . The total tax was . The nightly cost (excluding tax) to stay at the hotel in Paris was more than the nightly cost (excluding tax) to stay in Oslo. Find the cost per night for each hotel excluding tax.

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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x