As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge o
f 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?
<span>Given: P = (20 + 0.5x) + 0.15(20 + 0.5x)</span>
$62.10 is the maximum budget Jennifer can spend. So, The maximum price a book can have would be $62.10 <span>Substituting the value of P in the equation: </span> <span>P = (20 + 0.5x) + 0.15(20 + 0.5x) </span> <span>P = $ 62.10 Therefore, $62.10 = (20 + 0.5x) + 0.15(20 + 0.5x) </span> <span> Now solving for x we get: </span> <span>62.10 = 20 + 0.5x + 0.15(20) + 0.15(0.5x) </span> <span>62.10 = 20 + 0.5x + 3 + 0.075x Adding the like terms: </span> <span>62.10 = (0.5x + 0.075x) + (20 + 3) </span> <span>62.10 = 0.575x + 23 </span>subtracting 23 from both sides: we get, <span>39.10 = 0.575x dividing both sides by 0.575 </span> x = 68 As x represents the number of pages,so <span>the maximum number of pages she can have in her book is 68.</span>
