A traveler just returned from Europe spent $30 a day for housing in England, $20 a day in France and $20 a day in Spain. For food, the traveler spent $10 a day in each country for incidental expenses?
The traveler's records of the trip indicate a total of $340 spent for housing,$320 for food and $140 for incidental expenses while traveling in these countries. calculate the number of days the traveler spent in each of the countries or show that the records must be incorrect, because the amounts spent are incompatible with each other.
The traveler's records of the trip indicate a total of $340 spent for housing,$320 for food and $140 for incidental expenses while traveling in these countries. calculate the number of days the traveler spent in each of the countries or show that the records must be incorrect, because the amounts spent are incompatible with each other.
1 Answer
The numbers are incompatible.
Explanation:
Let's call E, the number of days he spent in England, F, the number of says in France and S the number of days in Spain.
The first sentence, coupled with the supposed $340 expenditure in housing would give us the following equation:
The $10 food per day in each locale, plus the $320 total would give us the following equation:
With these two equations, assuming that each of the day totals (E, F and S) are greater than zero (because we can't have negative days), we should get meaningful results when we operate on them.
First we could multiply the second equation by two:
And then we could subtract that equation from the first one:
As we can see, the F totals and the S totals cancel out leaving us with:
That would mean that the traveler would have to spend negative 30 days in England in order for those two equations to be compatible. As we know, we can't travel back in time, so the numbers have to be wrong.
