Two Variable equations/ word problem

Question

As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge of 15%. The price of a book can be modeled by the equation below, where P = the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x = the number of pages:

P = (20 + 0.5x) + 0.15(20 + 0.5x)

Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book?

x = ______________________ pages

Answer 1

Hi

First, use the distributive property to simplify 0.15(20+0.5x)=0.15•20 + 0.15•0.5x

                                                                                      =3 + 0.075x

 

combine like terms:       20 + 0.5x + 3 + 0.075x = 23 + .575x

 

the amount she can spend on a purchase is P = 23 + 0.575x,  P =  $62.10 so the equation is

 

                                                                62.10 = 23 + 0.575x

use the subtraction property of equality      -23.00    -23_______

 

Subtract and bring down                              39.10 = 0 + 0.575x

 

Simplify                                                      39.10 = 0.575x

                                                                  0.575    0.575

use the division property of equality

to divide both sides of the = sign by

the co-efficient of x, 0.575                                68 = x

 

Jennifer can buy a book that has 68 pages for $62.10.

 

                                                                   

Answer 2

Alexis, to solve this set P=62.10 and solve for x.

62.10=20+0.5x+3+.075x

62.10=23+.575x

39.1=.575x

x=68

 

Checking our work:

20+.5*68+.15(20+.5*68)=20+34+.15(20+34)=54+.15(54)=54+8.1=62.1

 

Hope that helps!