An executive of trident communications recently traveled to london, paris, and rome. He paid 180$, 230$, and 160$ per night for lodging in london, paris, and rome, respectively, and his hotel bills totaled 2660$. He spent 110$, 120$, and 90$ per day for his meals in london, paris, and rome, respectively, and his expenses for meals totaled 1520$. If he spent as many days in london as he did in paris and rome combined, how many days did he stay in each city ?
what have they told you?
l = p+r
180l+230p+160r = 2660
110l+120p+90r = 1520
Now just solve for l,p,r.
Ah, the executive's globe-trotting adventure! So, let's break it down.
First, we know that the total hotel bill was $2660, and he paid $180, $230, and $160 per night for lodging in London, Paris, and Rome, respectively.
To figure out how many nights he stayed in each city, we can divide the total bill by the nightly cost:
- In London: $2660 / $180 = 14.78 nights (let's say he stayed for 15 nights)
- In Paris: $2660 / $230 = 11.56 nights (let's say he stayed for 12 nights)
- In Rome: $2660 / $160 = 16.63 nights (let's say he stayed for 17 nights)
Now, let's move on to the meals. His meal expenses totaled $1520, and he spent $110, $120, and $90 per day for meals in London, Paris, and Rome, respectively.
To find out how many days he stayed in each city, we can divide the total meal expenses by the daily cost:
- In London: $1520 / $110 = 13.81 days (let's say he stayed for 14 days)
- In Paris: $1520 / $120 = 12.67 days (let's say he stayed for 13 days)
- In Rome: $1520 / $90 = 16.89 days (let's say he stayed for 17 days)
Now, we're given that he spent as many days in London as he did in Paris and Rome combined. So, we can set up an equation:
Days in London = Days in Paris + Days in Rome
Let's use the rounded values we got earlier:
14 = 13 + 17
But that's not true! So let's try adjusting our rounded values until we find a solution:
14 = 12 + 17
14 = 12 + 16
14 = 12 + 15
14 = 13 + 16
14 = 13 + 15
14 = 14 + 14
Aha! We found a solution. Since he spent 14 days in London, 13 days in Paris, and 14 days in Rome, he stayed in each city for those respective durations.
Let's break down the information given to solve the problem step by step:
1. Let's assume the executive stayed for 'x' number of days in London.
2. According to the given information, he stayed for 'x' number of days in Paris and Rome combined.
3. The total lodging cost for London is $180 per night, so the lodging cost for 'x' number of days in London is $180x.
4. The total lodging cost for Paris is $230 per night, so the lodging cost for 'x' number of days in Paris is $230x.
5. The total lodging cost for Rome is $160 per night, so the lodging cost for 'x' number of days in Rome is $160x.
6. The total lodging cost for all three cities is given as $2660.
Therefore, we can write the equation: $180x + $230x + $160x = $2660.
7. Let's solve the equation to find the value of 'x':
Combining like terms, we have: $570x = $2660.
Dividing both sides by $570, we get: x = $2660 / $570 = 4.667.
Since 'x' represents the number of days, we can round it to the nearest whole number. Therefore, x ≈ 5.
8. Hence, the executive stayed for 5 days in London.
9. He stayed for 'x' number of days in Paris and Rome combined, which is also 5 days.
Therefore, the executive stayed for 5 days in each city: 5 days in London, 5 days in Paris, and 5 days in Rome.
To determine how many days the executive stayed in each city, we can set up a system of equations based on the given information.
Let's assume the executive stayed in London for x days. Therefore, he stayed in Paris and Rome for the combined number of days, which is (x + x) = 2x days.
We can set up two equations using the given information:
Equation 1: Total lodging expenses = (lodging cost per night in London * number of days in London) + (lodging cost per night in Paris * number of days in Paris) + (lodging cost per night in Rome * number of days in Rome)
2660 = (180x) + (230 * 2x) + (160 * 2x)
Equation 2: Total meal expenses = (meal cost per day in London * number of days in London) + (meal cost per day in Paris * number of days in Paris) + (meal cost per day in Rome * number of days in Rome)
1520 = (110x) + (120 * 2x) + (90 * 2x)
By simplifying and solving these equations, we can determine the value of x, which represents the number of days the executive stayed in London.
Starting with Equation 1:
2660 = 180x + 460x + 320x
Combining like terms:
2660 = 960x
Dividing both sides by 960:
x = 2660 / 960
x ≈ 2.77
Since we can't have a fractional number of days, we'll round up to the nearest whole number:
x = 3
Therefore, the executive stayed in London for 3 days. Since he stayed in Paris and Rome for the combined number of days (2x), he stayed in each of those cities for 2 * 3 = 6 days.
In conclusion, the executive stayed in London for 3 days and in both Paris and Rome for 6 days each.