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Mark is attempting to build muscle mass and so he needs to eat at least an additional 80 grams of protein a day. A bottle of protein water costs $3.20 and a protein bar costs $1.75. The protein water supplies 27 grams of protein and the bar supplies 16 gram. If he has $ 10 dollars to spend

Write a system of inequalities to model this situation.
Graph the system.
Could he buy 3 bottles of protein water and 1 protein bar?
Could he buy no bottles of protein water and 5 protein bars?

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Jocelyn desires to increase both her protein consumption and caloric intake. She desires to have at least 35 more grams of protein each day and no more than an additional 200 calories daily. An ounce of cheddar cheese has 7 grams of protein and 110 calories. An ounce of parmesan cheese has 11 grams of protein and 22 calories.

Write a system of inequalities to model this situation.
Graph the system.
Could she eat 1 ounce of cheddar cheese and 3 ounces of parmesan cheese?
Could she eat 2 ounces of cheddar cheese and 1 ounce of parmesan cheese?

  1. { 7 c + 11 p 35 110 c + 22 p 200

  2. This figure shows a graph on an x y-coordinate plane of 7c + 11p is greater than or equal to 35 and 110c + 22p is less than or equal to 200. The area to the left or right of each line is shaded different colors with the overlapping area also shaded a different color.
  3. Yes
  4. No
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Mark is increasing his exercise routine by running and walking at least 4 miles each day. His goal is to burn a minimum of 1,500 calories from this exercise. Walking burns 270 calories/mile and running burns 650 calories.

Write a system of inequalities to model this situation.
Graph the system.
Could he meet his goal by walking 3 miles and running 1 mile?
Could he meet his goal by walking 2 miles and running 2 mile?

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Everyday math

Tickets for an American Baseball League game for 3 adults and 3 children cost less than $75, while tickets for 2 adults and 4 children cost less than $62.

Write a system of inequalities to model this problem.
Graph the system.
Could the tickets cost $20 for adults and $8 for children?
Could the tickets cost $15 for adults and $5 for children?

  1. { 3 a + 3 c < 75 2 a + 4 c < 62

  2. This figure shows a graph on an x y-coordinate plane of 3a + 3c is less than 75 and 2a + 4c is less than 62. The area to the left ofeach line is shaded different colors with the overlapping area also shaded a different color. Both lines are dotted.
  3. No
  4. Yes
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Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets.

Write a system of inequalities to model this situation.
Graph the system.
Could they take 9 children and 4 adults to both shows?
Could they take 8 children and 5 adults to both shows?

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Writing exercises

Graph the inequality x y 3 . How do you know which side of the line x y = 3 should be shaded?

Answers will vary.

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Graph the system { x + 2 y 6 y 1 2 x 4 . What does the solution mean?

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has four columsn and four rows. The columns are labeled, “I can………,” “confidently.” “with some help.” “no – I don’t get it!” The only rows filled in are under the “I can……...” column. The rows say, “determine whether an ordered pair is a solution of a system of linear inequalities.” “solve a system of linear inequalities by graphing.” and “solving applications of systmes of inequalities.”

After reviewing this checklist, what will you do to become confident for all objectives?

Section 5.1 Solve Systems of Equations by Graphing

Determine Whether an Ordered Pair is a Solution of a System of Equations .

In the following exercises, determine if the following points are solutions to the given system of equations.

{ x + 3 y = −9 2 x 4 y = 12

( −3 , −2 ) ( 0 , −3 )

no yes

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{ x + y = 8 y = x 4

( 6 , 2 ) ( 9 , −1 )

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Practice Key Terms 1

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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