Chapter ISG, Problem 5.6.6P

a.

To determine

To write an inequality equation.

Answer to Problem 5.6.6P

  

Explanation of Solution

Given information:

Video cost $2.5 each

Song cost $1.25 each

K has $50 card.

Number of songs is 's'

Number of videos is 'v'

Calculation:

One video cost =2.5

One song cost=1.25

'v' videos cost=2.5v

's' songs cost=1.25s

According to question

Cost constraints:

b.

To determine

To graph the solution of inequality.

  

Answer to Problem 5.6.6P

  

Explanation of Solution

Given information:

  

Calculation:

  

Rewrite

  

Slope intercept form

  

slope=-2

Means -2 unit change in y-coordinate with respect to 1 unit change in x-coordinate

Y-intercept: (0,40)

Ordinary equation

  

Substituting x=0

Then y=40

Substituting y=0

Then x=20

Table of x and y is given below

  

Then graph is given below

  

Region

Take a point below the line

Point (-10,10) is below line put in inequlity equation

  

On solving,

  is true

Then graph of inequality is given below

  

c.

To determine

To write three combination of songs and videos using graph.

Answer to Problem 5.6.6P

Three combinations of songs and videos

(20,0) , (10,20) , and (0,40)

Explanation of Solution

Given information:

  

Three combinations of songs and videos

(20,0) , (10,20) , and (0,40)

d.

To determine

To find money left in card.

Answer to Problem 5.6.6P

When k download 13 songs and 13 videos

$1.25 left on card.

Explanation of Solution

Given information:

Video cost $2.5 each

Song cost $1.25 each

K has $50 card.

Number of songs is 's'

Number of videos is 'v'

Inequality equation

  

Calculation:

  

When k download 13 songs and 13 videos

Songs, s=13

Videos, v=13

Substituting values of s and v in the inequality equation

  

On solving,

  

On solving,

  

Money left=50-48.75=1.25

Hence, a $1.25 left on card.