4.1+Comparing+Costs+0910

A.R. May 2, 2010 Big Idea - Equations can be used to model real things Essential Question - How do I create and solve equations?

Problem 4.1 and Follow up

** A. Make a table of X and Y values for each bid. Use your table to find the number of books for which the two bids are equal. Explain. **


 * ** No. of Books ** || ** Bid 1 ** || ** Bid 2 ** ||
 * 0 || 100 || 25 ||
 * 1 || 104 || 32 ||
 * 2 || 108 || 39 ||
 * 3 || 112 || 46 ||
 * 4 || 116 || 53 ||
 * 5 || 120 || 60 ||
 * 6 || 124 || 67 ||
 * 7 || 128 || 74 ||
 * 8 || 132 || 81 ||
 * 9 || 136 || 88 ||
 * 10 || 140 || 95 ||
 * 11 || 144 || 102 ||
 * 12 || 148 || 109 ||
 * 13 || 152 || 116 ||
 * 14 || 156 || 123 ||
 * 15 || 160 || 130 ||
 * 16 || 164 || 137 ||
 * 17 || 168 || 144 ||
 * 18 || 172 || 151 ||
 * 19 || 176 || 158 ||
 * 20 || 180 || 165 ||
 * 21 || 184 || 172 ||
 * 22 || 188 || 179 ||
 * 23 || 192 || 185 ||
 * 24 || 196 || 193 ||
 * 25 || 200 || 200 ||
 * B. Make a graph of the two equations. Use your graph to find out the number of books for which the two bids are equal. Copy the graph onto your paper and use it to explain how you found your answer.**




 * C. For what numbers of books is bid 1 less than bid 2? Explain how you found your answer.**

Bid 1 is cheaper after 25 books because after 25, bid 2 will increase by 7 each time whereas bid 1 will only increase by 4 each time thus making it cheaper after 25 books.

1. For each bid, find the cost of printing 75 books. Explain how you found your answer.** 100 + 4x 100 + 4 x 75 100 + 300 400 || Bid 2: 25 + 7x 25 + 7 x 75 25 + 525 550 ||
 * Follow Up
 * Bid 1:




 * 2. For each bid, find the the greatest number of books that can be printed if the cost is not to exceed $300. Explain.**

For bid 1, the greatest number of books that does not exceed $300 is 50. For bid 2, the greatest number of books that does not exceed $300 is 39.

|| Bid 1: 100 + 4x 100 + 4 x 50 100 + 200 300 ||

|| Bid 2: 25 + 7x 25 + 7 x 39 25 + 273 298 ||

bid 3 = 8 x the number of books to print bid 4 = 30 + 6 x the number of books to print**
 * 3. The club decides to request bids from two more printers.

At 15, both bid 3 and 4 will be equal.


 * ** No. of Books ** || ** Bid 3 ** || ** Bid 4 ** ||
 * 0 || 0 || 30 ||
 * 1 || 8 || 36 ||
 * 2 || 16 || 42 ||
 * 3 || 24 || 48 ||
 * 4 || 32 || 54 ||
 * 5 || 40 || 60 ||
 * 6 || 48 || 66 ||
 * 7 || 56 || 72 ||
 * 8 || 64 || 78 ||
 * 9 || 72 || 84 ||
 * 10 || 80 || 90 ||
 * 11 || 88 || 96 ||
 * 12 || 96 || 102 ||
 * 13 || 104 || 108 ||
 * 14 || 112 || 114 ||
 * 15 || 120 || 120 ||