MathMaster logo

MathMaster

  1. Home
  2. general
  3. 2 solve the following problems with the support of determinants a the tourist company mi bonito michoacan hired an adverti
Question

2. Solve the following problems with the support of determinants a) The tourist company “Mi bonito Michoacán” hired an advertising company to Create a poster promoting a tour of the main magical towns in the state of Michoacán. The tour consists of visiting the magical towns of Michoacán for 14 nights. Tacámbaro, Patzcuaro, Jiquilpan and Santa Clara del Cobre. The cost per night of lodging is $120, $200, $80 and $100, respectively, and their total expense for the concept lodging is $2020. The number of days offered in Pátzcuaro will be the same as the total number of days they will spend in Tacámbaro and Santa Clara del Cobre; in addition, will spend three times more days in Pátzcuaro than in Jiquilpan. The advertising company requires all the necessary information to be able to make the poster, which is why it is necessary know How many days will customers spend in each town?

92

likes
461 views

Answer to a math question 2. Solve the following problems with the support of determinants a) The tourist company “Mi bonito Michoacán” hired an advertising company to Create a poster promoting a tour of the main magical towns in the state of Michoacán. The tour consists of visiting the magical towns of Michoacán for 14 nights. Tacámbaro, Patzcuaro, Jiquilpan and Santa Clara del Cobre. The cost per night of lodging is $120, $200, $80 and $100, respectively, and their total expense for the concept lodging is $2020. The number of days offered in Pátzcuaro will be the same as the total number of days they will spend in Tacámbaro and Santa Clara del Cobre; in addition, will spend three times more days in Pátzcuaro than in Jiquilpan. The advertising company requires all the necessary information to be able to make the poster, which is why it is necessary know How many days will customers spend in each town?

Expert avatar
Birdie
4.5
103 Answers
1. Let \( x_1 \), \( x_2 \), \( x_3 \), \( x_4 \) be the number of days spent in Tacámbaro, Pátzcuaro, Jiquilpan, and Santa Clara del Cobre respectively.
2. We have the following system of linear equations:

\[
\begin{cases}
x_1 + x_2 + x_3 + x_4 = 14 \\
120x_1 + 200x_2 + 80x_3 + 100x_4 = 2020 \\
x_2 = x_1 + x_4 \\
x_2 = 3x_3
\end{cases}
\]

3. Substituting \( x_2 = x_1 + x_4 \) and \( x_2 = 3x_3 \) into the equations:

\[
x_1 + (x_1 + x_4) + x_3 + x_4 = 14 \\
120x_1 + 200(x_1 + x_4) + 80x_3 + 100x_4 = 2020
\]

4. Simplify each equation:

\[
2x_1 + x_3 + 2x_4 = 14 \\
320x_1 + 200x_4 + 80x_3 = 2020
\]

Understanding from equation \( x_2 = 3x_3 \):

Replace \( x_2 \) & Simplify the system.

Let's denote the determinant

A = \begin{vmatrix} 1 & 1 & 1 & 1 \\ 120 & 200 & 80 & 100 \\ 0 & -1 & 0 & 1 \\ 0 & -3 & 1 & 0 \end{vmatrix}

Calculate it and solution from

X = A^{-1}

From there,

5. Solve the equations to get exact days for each city:

x_1 = \frac{290}{7}, \quad x_2 = \frac{580}{7}, \quad x_3 = \frac{290}{21}, \quad x_4 = \frac{290}{21}

Frequently asked questions (FAQs)
What is the product of the mixed number 3 ¼ and the real number 1.5, when factoring the numbers involved?
+
What is the value of sinh(cos(-3)) - tanh(2) when the hyperbolic functions are evaluated using radians?
+
Math question: Find the x-coordinate of the vertical asymptote of the reciprocal function f(x) = 1/x.
+
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
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
How many percent is one second out a 24 hour?
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
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=_____
If 0101, what is the binary representation of the 4x16 decoder output?
Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:
2x+4x=
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one
Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?
Show work on 4108 divided by 4
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.
suppose a city with population 80,000 has been growing at a rate of 8% per year if this rate continues find the population of this city in 10 years
How do you convert a fraction to a decimal
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
4m - 3t + 7 = 16
-1/3x+15=18
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].

You might be interested in