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 product of 26 multiplied by 47?
+
What is the period of the trigonometric function f(x) = 2cos(3x) + sin(5x) - tan(2x) - cot(4x)?
+
What is the equation for a logarithmic function that passes through the points (1, 5) and (4, 15)?
+
New questions in Mathematics
A=m/2-t isolate t
X^2 = 25
[(36,000,000)(0.000003)^2]divided(0.00000006)
Analyze the following situation Juan is starting a new business, he indicates that the price of his product corresponds to p=6000−4x , where x represent the number of tons produced and sold and p It is given in dollars. According to the previous information, what is the maximum income that Juan can obtain with his new product?
According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card
You mix a powder drug with a 4.5ml of liquid to get a reconstituted solution with a concentration of 250mg/ml. The prescribers order is for 500 mg . You will give what ml of the reconstituted solution
User The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm. How tall is Lili?
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
Oi👋🏻 Toque em "Criar Nova Tarefa" para enviar seu problema de matemática. Um dos nossos especialistas começará a trabalhar nisso imediatamente!
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
It costs a manufacturer $2,500 to purchase the tools to manufacture a certain homemade item. If the cost for materials and labor is 60¢ per item produced, and if the manufacturer can sell each item for 90¢, find how many items must he produce and sell to make a profit of $2000?
6(k-7) -2=5
A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed. (a) How many cubic feet of water can the pool hold? cubic feet (b) The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this? cubic feet
f(r) = 1/r+9 find f(x^2) + 1
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.