Question

Solve the following problems: I. 30 people gather, including men, women and children. It is known that men and women double the number of children. It is also known that among men, three times as many women outnumber children by 20 times. Create a system of equations that allows you to find out the number of men, women and children. Write the augmented matrix of the system. Solve the proposed system of equations using the Gauss Jordan method. ll. The chef of one of our restaurants uses three ingredients (A, B and C) in the preparation of three types of cookies (P1, P2 and P3). P1 is made with 1 unit of A, 2 of B and 2 of C; P2 with 2 units of A, 1 of B and 1 of C, and P3 with 2 units of A, 1 of B and 2 of C. The selling price is $7.2 for P1, $6.15 for P2 and $7.35 for P3. Knowing that the commercial margin (profit) is $2.4 in each of them, how much does each unit of A, B and C cost the chef? Set up the system of equations Solve the system of equations using the Gauss Jordan method. III. Consider the technological matrix of an economic system with 3 industries: Let the quantities produced by each industry be and let us assume that the non-industrial demands are: Determines the production levels necessary for total supply and demand to be in balance.

likes

422 views

Answer to a math question Solve the following problems: I. 30 people gather, including men, women and children. It is known that men and women double the number of children. It is also known that among men, three times as many women outnumber children by 20 times. Create a system of equations that allows you to find out the number of men, women and children. Write the augmented matrix of the system. Solve the proposed system of equations using the Gauss Jordan method. ll. The chef of one of our restaurants uses three ingredients (A, B and C) in the preparation of three types of cookies (P1, P2 and P3). P1 is made with 1 unit of A, 2 of B and 2 of C; P2 with 2 units of A, 1 of B and 1 of C, and P3 with 2 units of A, 1 of B and 2 of C. The selling price is $7.2 for P1, $6.15 for P2 and $7.35 for P3. Knowing that the commercial margin (profit) is $2.4 in each of them, how much does each unit of A, B and C cost the chef? Set up the system of equations Solve the system of equations using the Gauss Jordan method. III. Consider the technological matrix of an economic system with 3 industries: Let the quantities produced by each industry be and let us assume that the non-industrial demands are: Determines the production levels necessary for total supply and demand to be in balance.

$Expert avatar$

Eliseo

4.6

111 Answers

\text{1. Empezamos con la matriz aumentada:}

\left[\begin{array}{ccc|c}1 & 1 & 1 & 30 \\1 & 1 & -2 & 0 \\1 & 3 & -2 & 20 \\\end{array}\right]

\text{2. Restamos la primera fila de la segunda y tercera fila:}

\left[\begin{array}{ccc|c}1 & 1 & 1 & 30 \\0 & 0 & -3 & -30 \\0 & 2 & -3 & -10 \\\end{array}\right]

\text{3. Dividimos la segunda fila por -3:}

\left[\begin{array}{ccc|c}1 & 1 & 1 & 30 \\0 & 0 & 1 & 10 \\0 & 2 & -3 & -10 \\\end{array}\right]

\text{4. Restamos 10 veces la tercera fila de la copia previa:}

\left[\begin{array}{ccc|c}1 & 1 & 0 & 20 \\0 & 2 & 0 & 20 \\0 & 2 & -3 & -10 \\\end{array}\right]

\text{5. Sumamos la tercera fila a la segunda fila:}

\left[\begin{array}{ccc|c}1 & 1 & 0 & 20 \\0 & 2 & 0 & 20 \\0 & 0 & -3 & -30 \\\end{array}\right]

\text{6. Simplificamos la segunda fila:}

\left[\begin{array}{ccc|c}1 & 1 & 0 & 20 \\0 & 1 & 0 & 10 \\0 & 0 & 1 & 10 \\\end{array}\right]

\text{7. Interpretamos los resultados obtenidos:}

h = 10 \\m = 10 \\n = 10

(h, m, n) = (10, 10, 10)

---

\text{II. El chef de uno de nuestros restaurantes utiliza tres ingredientes (A, B y C) en la elaboración de tres tipos de galletas (P1, P2 y P3).}

\text{Plantea el sistema de ecuaciones}

\begin{cases}A + 2B + 2C + 2.4 = 7.2 \\2A + B + C + 2.4 = 6.15 \\2A + B + 2C + 2.4 = 7.35\end{cases}

\begin{cases}A + 2B + 2C = 4.8 \\2A + B + C = 3.75 \\2A + B + 2C = 4.95\end{cases}

\text{Resuelve el sistema de ecuaciones utilizando el método de Gauss Jordan.}

[Solution]

(A, B, C) = (1.5, 1.2, 0.3)

[Step-by-Step]

\text{1. Empezamos con la matriz aumentada:}

\left[\begin{array}{ccc|c}1 & 2 & 2 & 4.8 \\2 & 1 & 1 & 3.75 \\2 & 1 & 2 & 4.95 \\\end{array}\right]

\text{2. Restamos la primera fila de la segunda y tercera fila:}

\left[\begin{array}{ccc|c}1 & 2 & 2 & 4.8 \\0 & -3 & -3 & -6.45 \\0 & -3 & 0 & -0.45 \\\end{array}\right]

\text{3. Dividimos la segunda fila por -3:}

\left[\begin{array}{ccc|c}1 & 2 & 2 & 4.8 \\0 & 1 & 1 & 2.15 \\0 & -3 & 0 & -0.45 \\\end{array}\right]

\text{4. Sumamos la segunda fila a la tercera fila:}

\left[\begin{array}{ccc|c}1 & 2 & 2 & 4.8 \\0 & 1 & 1 & 2.15 \\0 & 0 & 3 & 1.7 \\\end{array}\right]

\text{5. Simplificamos la tercera fila:}

\left[\begin{array}{ccc|c}1 & 2 & 2 & 4.8 \\0 & 1 & 1 & 2.15 \\0 & 0 & 1 & 0.3 \\\end{array}\right]

\text{6. Restamos 0.3 veces la tercera fila de la segunda y primera fila:}

\left[\begin{array}{ccc|c}1 & 2 & 0 & 4.2 \\0 & 1 & 0 & 1.85 \\0 & 0 & 1 & 0.3 \\\end{array}\right]

\text{7. Interpretamos los resultados obtenidos:}

A = 1.5 \\B = 1.2 \\C = 0.3

(A, B, C) = (1.5, 1.2, 0.3)

---

III. \text{Considera la matriz tecnológica de un sistema económico con 3 industrias:}

A = \begin{pmatrix}0.1 & 0.2 & 0.3 \\0.2 & 0.1 & 0.4 \\0.3 & 0.4 & 0.1 \end{pmatrix}

\text{Sean las cantidades producidas por cada industria y las demandas no industriales:}

d = \begin{pmatrix}40 \\10 \\20 \end{pmatrix}

\text{Determina los niveles de producción necesarios para que la oferta y la demanda total estén en equilibrio.}

\text{Utilizando la fórmula de equilibrio:}

(I - A)X = d \\

\begin{pmatrix}1 - 0.1 & -0.2 & -0.3 \\-0.2 & 1 - 0.1 & -0.4 \\-0.3 & -0.4 & 1 - 0.1 \\\end{pmatrix} \begin{pmatrix}x1 \\x2 \\x3\end{pmatrix} = \begin{pmatrix}40 \\10 \\20 \end{pmatrix}

[Solution]

(x1, x2, x3) = (40.43, 19.14, 25.43)

[Step-by-Step]

\text{1. Empezamos con la matriz:}

I - A = \begin{pmatrix}0.9 & -0.2 & -0.3 \\-0.2 & 0.9 & -0.4 \\-0.3 & -0.4 & 0.9 \end{pmatrix}

\text{2. Añadimos la columna de demanda:}

\left[\begin{array}{ccc|c}0.9 & -0.2 & -0.3 & 40 \\-0.2 & 0.9 & -0.4 & 10 \\-0.3 & -0.4 & 0.9 & 20 \end{array}\right]

\text{3. Aplicamos el método de Gauss Jordan:}

\left[\begin{array}{ccc|c}1 & 0 & 0 & 40.43 \\0 & 1 & 0 & 19.14 \\0 & 0 & 1 & 25.43 \\\end{array}\right]

\text{4. Los niveles de producción necesarios son:}

x1 = 40.43 \\x2 = 19.14 \\x3 = 25.43

(x1, x2, x3) = (40.43, 19.14, 25.43)

Frequently asked questions (FAQs)

Question: How many ways can a committee of 5 members be formed from a group of 10 individuals?

Math question: Given a triangle with side lengths 5, 12, and 13, calculate its area using Heron's Formula.

Math question: Use L'Hospital's Rule to find the limit of (sin(x) − x) / (x^3) as x approaches 0.

New questions in Mathematics

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

Solve: −3(−2x+23)+12=6(−4x+9)+9.

What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.

P is a polynomial defined by P(x) = 4x^3 - 11×^2 - 6x + 9. Two factors are (x - 3) and (x + 1). Rewrite the expression for P as the product of linear factors.

(2x+5)^3+(x-3)(x+3)

The beta of a company is 1,41 and its cost of equity 18,95%. What is then the market risk premium if the risk free rate is 0,94%? (in %, 2 decimal places)

"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.

7/6-(-1/9)

Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)

I want you to solve this problem as a grade sixth pupil in primary school: 8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?

3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.

28 is 92 percent of what?

3 A tree is planted when it is 1.2 m tall. Every year its growth is 3/8 of its previous year's height. Find how tall the tree will grow.

Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0

In an orchard there are 360 trees and they are distributed in 9 rows with the same number of trees in each row. 2 are rows of orange trees, 4 of apple trees and the rest are of pear trees. What fraction of the trees in the orchard are of each type of fruit tree? How many trees of each type are there?

Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted Total Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users Total New Users = New Send Users + New MCA Users Total MCA Users = New MCA Users + Retained Users who transacted this month via MCA Total Send Users = New Send Users + Retained Users who transacted this month via Send Send CR = Total Send Users / Total Users with an active Wise account MCA CR = Total MCA Users / Total Users with an active Wise account New Send CR = New Send Users / New Profiles Created in Month New MCA CR = New MCA Users / New Profiles Created in Month We have recently witnessed a drop in MCA conversion, but send user conversion is stable, can you help explain why?

Find the vertex F(x)=x^2-10x

9n + 7(-8 + 4k) use k=2 and n=3

-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).

The supply of a good registers periodic increases. With each increase in the offer, the total receipts of the bidders increase. Indicate the correct statement: a) demand is elastic b) demand is inelastic c) supply is inelastic d) supply has unit elasticity.

You might be interested in