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?

151

likes
754 views

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?

Expert avatar
Timmothy
4.8
97 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 minutes, with the amount being 5425 pesos.

Frequently asked questions (FAQs)
What is the prime factorization of the mixed number 5⅔?
+
Math question: What is the vertex of the quadratic function y = -2(x-3)^2 + 5?
+
What is the formula to find the area of a regular hexagon, given the length of one side?
+
New questions in Mathematics
Find 2 numbers that the sum of 1/3 of the first plus 1/5 of the second will be equal to 13 and that if you multiply the first by 5 and the second by 7 you get 247 as the sum of the two products with replacement solution
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
-8+3/5
X^2 = 25
The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____
Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years? Round your answer to the nearest cent.
If f(x) = 3x 2, what is the value of x so that f(x) = 11?
Identify a pattern in the list of numbers.Then use this pattern to find the next number. 37,31,25,19,13
4. Show that if n is any integer, then n^2 3n 5 is an odd integer
is the x element (180,270), if tanx-3cotx=2, sinx ?
Convert 78 percent to a decimal
78 percent to a decimal
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? $14,900 $3725 $$37250 $18625
Oi👋🏻 Toque em "Criar Nova Tarefa" para enviar seu problema de matemática. Um dos nossos especialistas começará a trabalhar nisso imediatamente!
Evaluate ab+dc if a=56 , b=−34 , c=0.4 , and d=12 . Write in simplest form.
6(k-7) -2=5
A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.
Suppose a car license plate consists of 2 letters and two digits of which the first cannot be zero. How many different plates can be engraved? consider only 26 letters and 10 digits draw an example of this.