BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 5, Problem 14CT

(a)

To determine

To graph: the inequality that represents the numbers of trophies and medals it can buy and interpret a solution of the inequality.

(a)

Expert Solution

Answer to Problem 14CT

The linear inequality is 12x+3y≤60 .

Explanation of Solution

Given:

The person wants to spend at most 60 dollar on trophies and medals. The trophy is 12 dollar each and the medal is 3 dollar each.

Concept used:

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but the are of the coordinate plane that satisfy the inequality.

The boundary line is dashed for <or > and solid line for ≤or ≥ .

The common area is the solution of inequality.

Calculation:

The person wants to spend at most 60 dollar on trophies and medals. The trophy is 12 dollar each and the medal is 3 dollar each.

Write the inequality and draw the graph.

If it wants purchase at least 6 items, write and draw the system of linear inequalities, determine how many of each item it can be purchased.

Let x be the number of trophies and y be the number of medals. Then the inequalities that models the purchase with at most 60 dollar is:

12x+3y≤60 .

Since, total amount is at most 60 dollars.

The linear inequality is 12x+3y≤60 .

Draw the graph of 12x+3y≤60 as show below. If only one item is purchase, either 20 trophies or 5 medal can be purchase as it is clear from the graph.

The graph of equation y≤−4x+20 :

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 5, Problem 14CT , additional homework tip 1

Hence, the linear inequality is 12x+3y≤60 .

(b)

To determine

To graph: the system that represents the situation and find the number of item that person can buy.

(b)

Expert Solution

Answer to Problem 14CT

The graph of system of linear inequalities is drawn.

Explanation of Solution

Given:

The person wants to spend at most 60 dollar on trophies and medals. The trophy is 12 dollar each and the medal is 3 dollar each.

Concept used:

The boundary line is dashed for <or > and solid line for ≤or ≥ .

The common area is the solution of inequality.

Calculation:

If it purchased at least 6 items then the system of inequalities is:

12x+3y≤60.x+y≥6.

Graph the inequalities x+y≥6 and 12x+3y≤60 as shown in the below figure. The intersection of blue and red colours represents the solutions set of given system of inequalities. The ordered pair (x,y)=(2,10) is in the solution set. It means it can buy 2 trophies and 10 medals.

The graph of inequalities y≤−4x+20,y≥−x+6 is:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 5, Problem 14CT , additional homework tip 2

Hence, the graph of system of linear inequalities is drawn.

Chapter 5, Problem 13CT

Chapter 5, Problem 15CT

Chapter 5 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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