3.4+Paying+Bills+and+Counting+Profits+0910

September 15, 2009 Math 7B SBK

Big Idea: Observation and description of changes in the world around us are the first steps in finding and learning about patterns.

INV 3 Essential Question: How can I visually explain situations where one thing changes based on another?
 * Problem 3.4 - Paying Bills and Counting Profit [[image:images.jpg]]**

Notes: The fraction bar __IS__ division, therefore you divide the numerator by the denominator when trying to find the decimal/percentage.


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


 * Number of Customers || Income || Bike Rental || Food and Camp Costs || Van Rental ||
 * 1 || $350 || $30 || $125 || $700 ||
 * 2 || 700 || 60 || 250 || 700 ||
 * 3 || 1,050 || 90 || 375 || 700 ||
 * 4 || 1,400 || 120 || 500 || 700 ||
 * 5 || 1,750 || 150 || 625 || 700 ||
 * 6 || 2,100 || 180 || 750 || 700 ||
 * 7 || 2,450 || 210 || 875 || 700 ||
 * 8 || 2,800 || 240 || 1,000 || 700 ||
 * 9 || 3,150 || 270 || 1,125 || 700 ||
 * 10 || 3,500 || 300 || 1,250 || 700 ||


 * B)** **How does the income column change as the number of costumers increases? Explain how you can use this relationship to calculate the income for any number of customers.**

Well, the more customers that pay, the more income you get. So, as the number of customers increases, the income increases as well. You take the number of customers, and multiply it by the income of only one person.


 * C) Add and complete a 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 increase? Describe how you can calculate the**
 * total cost for any number of customers.**


 * Number of Customers || Income || Bike Rental || Food and Camp Costs || Van Rental || Total Cost ||
 * 1 || $350 || $30 || $125 || $700 || $855 ||
 * 2 || 700 || 60 || 250 || 700 || 1,010 ||
 * 3 || 1,050 || 90 || 375 || 700 || 1,165 ||
 * 4 || 1,400 || 120 || 500 || 700 || 1,320 ||
 * 5 || 1,750 || 15 || 625 || 700 || 1,475 ||
 * 6 || 2,100 || 180 || 750 || 700 || 1,630 ||
 * 7 || 2,450 || 210 || 875 || 700 || 1,785 ||
 * 8 || 2,800 || 240 || 1,000 || 700 || 1,940 ||
 * 9 || 3,150 || 270 || 1,125 || 700 || 2,095 ||
 * 10 || 1,500 || 300 || 1,250 || 700 || 2,250 ||

The total cost increases as the number of people increases, because the more people they have, the more supplies all those people need. You would take the number of people, and then multiple that number by the original total cost. (If it’s something in the ten’s, divide it by ten, then multiply the van cost by that number.)


 * D) Add and complete a column for “Profit”. What profit would be earned for 5 customers? 10 customers? 25 customers?**


 * Number of Customers || Income || Bike Rental || Food and Camp Costs || Van Rental || Total Cost || Profit ||
 * 1 || $350 || $30 || $125 || $700 || $855 || $-505 ||
 * 2 || 700 || 60 || 250 || 700 || 1,010 || -310 ||
 * 3 || 1,050 || 90 || 375 || 700 || 1,165 || -115 ||
 * 4 || 1,400 || 120 || 500 || 700 || 1,320 || 80 ||
 * 5 || 1,750 || 150 || 625 || 700 || 1,475 || 275 ||
 * 6 || 2,100 || 180 || 750 || 700 || 1,630 || 470 ||
 * 7 || 2,450 || 210 || 875 || 700 || 1,785 || 665 ||
 * 8 || 2,800 || 240 || 1,000 || 700 || 1,940 || 860 ||
 * 9 || 3,150 || 270 || 1,125 || 700 || 2,095 || 1,055 ||
 * 10 || 3,500 || 300 || 1,250 || 700 || 2250 || 1250 ||

For five costumers, the profit would be $275. For ten customers the profit would be $2000. For 25 customers the profit would be $4,875. You take the total cost for the number of customers, and subtract that from the income.

Problem 3.4- Paying Bills and Counting Profits Follow Up


 * 1)** **What other patterns of change do you see in the table?**

The “Profit”, “Total cost”, and the “Van rental” columns are the only ones that don’t double in this table, while the “”Income”, “Bike rental”, and the “Food and camp costs” do double.


 * 2)** **What is the least number of customers needed for the tour to make a profit?**

You would need 4 customers to make some profit, because the income you make with 4 customers is enough to cover the damage done for the profit of the income of one customer.


 * 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.**

I would say 25 customers because even if you do make up for all the damage done, and it’s still a good amount of money for them to split among themselves.


 * [[image:math7c-2008:EJC_Square.png caption="EJC_Square.png"]] ||