The price of a hotel room in Helsinki is 159 euros/night. The exchange rates are 1 EUR = 1.0819 USD and 1 USD = 0.7732 GBP. Calculate the price of the room in British pounds (GBP). (EUR = euro, USD = American dollar, GBP = British pound) 2. Corrected_text: A company’s costs are divided into two parts, variable costs and fixed costs. The variable costs are 155,000€, which is 62% of the total costs. How many euros are the fixed costs? 3. Corrected_text: A small restaurant serves three different starters, four main dishes, and two desserts. The ingredients for one of the starters and one of the main courses have run out. A foreign customer, who does not understand the language of the menu, orders a full menu by randomly picking all three courses. What is the probability that the customer orders both the starter and the main course which cannot be made?
The Correct Answer and Explanation is:
Here are the correct answers and a detailed explanation for each of the three problems:
1. Converting 159 EUR to GBP using given exchange rates
- Given:
- 1 EUR = 1.0819 USD
- 1 USD = 0.7732 GBP
- Hotel price = 159 EUR
Step 1: Convert EUR to USD
159 EUR×1.0819 USD1 EUR=171.0261 USD159\ \text{EUR} \times \frac{1.0819\ \text{USD}}{1\ \text{EUR}} = 171.0261\ \text{USD}159 EUR×1 EUR1.0819 USD=171.0261 USD
Step 2: Convert USD to GBP
171.0261 USD×0.7732 GBP1 USD≈132.301 GBP171.0261\ \text{USD} \times \frac{0.7732\ \text{GBP}}{1\ \text{USD}} \approx 132.301\ \text{GBP}171.0261 USD×1 USD0.7732 GBP≈132.301 GBP
Answer: The price of the hotel room is approximately 132.30 GBP (rounded to 2 decimal places).
Explanation:
To convert the price of a hotel room from euros to British pounds, the exchange rates are applied in two steps. The euro amount is first multiplied by the EUR to USD conversion rate. The resulting value in USD is then multiplied by the USD to GBP conversion rate. This two-step method ensures the final result is in GBP. Maintaining correct significant figures and using accurate conversion factors yields the most reliable result.
2. Finding fixed costs when variable costs are 62% of total
- Variable costs = €155,000
- This represents 62% of total costs
Let T represent total costs.
Set up the equation:
0.62T=155,0000.62T = 155,0000.62T=155,000
Solve for T:
T=155,0000.62=250,000T = \frac{155,000}{0.62} = 250,000T=0.62155,000=250,000
Fixed costs = Total costs – Variable costs
Fixed costs = 250,000 – 155,000 = €95,000
Answer: The fixed costs are €95,000
Explanation:
The variable costs are known to be 62% of the total costs. By expressing this percentage relationship algebraically, the total cost can be found by dividing the variable cost amount by 0.62. Once the total cost is calculated, subtracting the variable costs gives the fixed portion. This approach separates each component of the cost structure and uses proportional reasoning to reach the answer.
3. Probability the customer picks both missing dishes
- 3 starters → 1 is unavailable → 2 available
- 4 main dishes → 1 is unavailable → 3 available
- 2 desserts → all available
- Total starter choices: 3
- Total main choices: 4
Only 1 specific starter and 1 specific main dish are unavailable.
Total possible combinations of full meals:
3 starters×4 mains×2 desserts=243 \text{ starters} \times 4 \text{ mains} \times 2 \text{ desserts} = 243 starters×4 mains×2 desserts=24
Only 1 combination includes both the unavailable starter and unavailable main course.
So, favorable outcomes = 1
Total outcomes = 24
Probability = 124\frac{1}{24}241
Answer: The probability is 124\frac{1}{24}241
Explanation:
The customer selects one dish from each category at random. Only one specific combination includes both the unavailable starter and the unavailable main course. By calculating the total number of possible three-course combinations and identifying the single unfavorable one, the desired probability is found by taking the ratio of the unfavorable case to the total. The dessert does not affect the outcome because both options are available.
