# To express: The given joint variation as equation.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.11, Problem 31E

(a)

To determine

## To express: The given joint variation as equation.

Expert Solution

The joint variation for given equation is C=k(mp) .

### Explanation of Solution

Cost of printing a magazine is jointly proportional to the number of pages p in magazine and number of magazine m .

Jointly proportional:

Consider the equation,

z=kxy .

Here, z is proportional to product of xy or z is jointly proportional to x and y both statements are same.

Here, k is constant of proportionality.

According to the given statement C is jointly proportional to p and m .

Write the given statement as,

C=k(mp) (1)

Here,

C is cost of printing the magazine.

p is number of pages in the magazine.

m is number of magazine printed.

k is constant of proportionality.

Thus, the equation of given statement is C=k(mp) .

(b)

To determine

### To find: The constant of proportionality k .

Expert Solution

The value of constant of proportionality is 18 .

### Explanation of Solution

Given:

Cost of printing (C) is $60,000 . Number of magazine (m) is 4000 . Number of pages in the magazine (p) is 120 . Calculation: Substitute$ 60,000 for C , 4000 for m and 120 for p in the equation (1).

60000=k(4000120)60000=k(480000)648=k18=k (2)

Thus, the value of proportionality constant k is 18 .

(c)

To determine

Expert Solution