Question
A transport company per application called "U" bases its rate on the time it takes to reach the destination, so that U(x) = x {2} + 180x + 300 , with X in minutes and U(x) in pesos. The transport company "C", which is directly responsible for the former, also sets its rates according to the duration of the transfer, so that C(x) = x (x + 192), with C(x) the amount to be paid in pesos, after X minutes since the car was boarded How many minutes should a trip take for the amount to be paid the same with either of these two applications and what is this amount?
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Answer to a math question A transport company per application called "U" bases its rate on the time it takes to reach the destination, so that U(x) = x {2} + 180x + 300 , with X in minutes and U(x) in pesos. The transport company "C", which is directly responsible for the former, also sets its rates according to the duration of the transfer, so that C(x) = x (x + 192), with C(x) the amount to be paid in pesos, after X minutes since the car was boarded How many minutes should a trip take for the amount to be paid the same with either of these two applications and what is this amount?
Timmothy
4.896 Answers
Given:
U(x) = x^2 + 180x + 300
C(x) = x(x + 192)
To find the common trip time \(x\) where the amount paid is the same for both companies:
U(x) = C(x)
x^2 + 180x + 300 = x(x + 192)
Solving the equation:
1. Set the equations equal to each other:
x^2 + 180x + 300 = x^2 + 192x
2. Subtract the \(x^2\) terms and simplify:
180x + 300 = 192x
300 = 192x - 180x
300 = 12x
x = \frac{300}{12}
x = 25
Therefore, the trip should take \(25\) minutes for the costs to be equal. Checking this in the original rate equations:
For \( U(x) \):
U(25) = 25^2 + 180 \cdot 25 + 300
U(25) = 625 + 4500 + 300
U(25) = 5425 \ \text{pesos}
For \( C(x) \):
C(25) = 25(25 + 192)
C(25) = 25 \cdot 217
C(25) = 5425 \ \text{pesos}
Both amounts match.
So the trip should take x = 25 5425
To find the common trip time \(x\) where the amount paid is the same for both companies:
Solving the equation:
1. Set the equations equal to each other:
2. Subtract the \(x^2\) terms and simplify:
Therefore, the trip should take \(25\) minutes for the costs to be equal. Checking this in the original rate equations:
For \( U(x) \):
For \( C(x) \):
Both amounts match.
So the trip should take
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