3.4+Paying+Bills+and+Counting+Profits+10-11

September 15, 2010 NO (Noel Oracheski)

=3.4 Paying Bills And Counting Profits =

**Essential Question:** How can I visually explain situations where one-thing changes based on another?

 * A. Copy Sidney’s table. Complete it to give information about income and estimated costs for up to 10 customers. **

Every time the number of customers increases the income also increases. For every customer the income increase would be $350. This is because that is how much each customer pays. If you wanted to quickly get to a certain amount of customers you just have to multiply the amount of customers by $350 and that will be the income for that amount of customers.
 * B. How does the income column change as the number of customers increases? Explain how you can use this relationship to calculate the income for any number of customers. **

 The total cost increases by $155 per customer. This can help you find the total cost of any amount of customers easily. You first subtract that number by 1 then divide it by $155 and then add $855. This is because the table starts at $855, not $155 
 * C.Add and complete column for “total cost” (including bike rental, food and camp costs, and van rental) to your table. How does the total cost change as the number of customers increases? Describe how you can calculate the total cost for any number of customers. **

For 5 customers the students profit would be only $275 and $1,250 dollars for 10 customers. Although if they had 25 customers they would earn $4,175. I found out how much money they would make for 25 customers by first subtracting 25 by 1 (getting the answer of 24.) Then I would multiply 24 and 195 (the amount the profit increases each time.) I would get $4,680. Lastly I would subtract $505 dollars because the table starts at -$505, not $195. In the end I would end up with $4,175. 
 * D. Add and complete a column for “profit.” What profit would be earned from a trip with 5 customers? 10 customers? 25 customers? **


 * Follow Up: **

There are many patterns in the table. First of all in the “bike rental” column for every customer it costs $30 more. Also in the “food and camp costs” column every increase in customer the cost increases too (by $125.) The “van rental” column stays at $700 dollars because not each person needs their own van. Under the “total costs” column every customer costs $155 more. And finally under the “profit” column the profit increased by $195 dollars per customer.
 * <span style="font-family: 'Comic Sans MS',cursive;">1. What other patterns of change do you see in the table? **

<span style="font-family: 'Comic Sans MS',cursive;">The least amount of customers that the students would need to make a profit would be 4 customers although then they are still only making $80.
 * <span style="font-family: 'Comic Sans MS',cursive;">2. What is the least amount of customers needed for the tour to make a profit? **

<span style="font-family: 'Comic Sans MS',cursive;">If they took 25 customers they would earn $4,175. Since there is 5 of them you divide that by 5 and each person would make $835, which is very reasonable.
 * <span style="font-family: 'Comic Sans MS',cursive;">3. What do you think is the least number of customers needed to make it worthwhile for the students to run the tour? Explain your answer. **


 * <span style="font-family: 'Comic Sans MS',cursive;">Notes: **
 * **<span style="font-family: 'Comic Sans MS',cursive;">Profit= Income-Costs **