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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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