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

07/09/10 NRM (nikhil) Observation and description Of Changes In The World Around Us Are The First Steps In Finding And Learning About Patterns. How can I visually explain situations where one thing changes based on another?

In class we learned different types of new vocabulary such as **income-** The total amount of money made in a business, **Profit-** the amount of money you have left after you subtract the costs from the income, I**ndependent And Dependent Variables -** which could be used in graphes and in tables usually placed on the X axis or Y axis on a graph. and on tables it would be the different columns, **costs-** the money spent in buying and supplying for the best. We have a diagram which tells us that you cannot subtract income from costs or you would end up with a negative number but you can subtract the costs from the income yes because then you would get the profit. A few questions i have about this problem is: Are there any other minor costs that they did not take in to consideration? Would this be a good business to continue? How would the graph look like if we made one using the data in the table?

A) **Copy Sidney's table. Complete it to give information about income and estimated cost for up to 10 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 income column increases by $350 for every customer. You could make a formula for example: you could let the number of customers be 'c' and since every time it is increasing by 350 the formula would be 350c. every time your replace c with the number of customers you would get the income. For instance you could replace c c with two customers and then times it by $350 and you would get the income which is $700.
 * Number of customers || Income || Bike Rental || Food and Camp Costs || Van Rental ||
 * 1 || $350 || $30 || $125 || $700 ||
 * 2 || 700 || 60 || 250 || 700 ||
 * 3 || 1050 || 90 || 500 || 700 ||
 * 4 || 1400 || 120 || 750 || 700 ||
 * 5 || 1750 || 150 || 875 || 700 ||
 * 6 || 2100 || 180 || 1000 || 700 ||
 * 7 || 2450 || 210 || 1125 || 700 ||
 * 8 || 2800 || 240 || 1250 || 700 ||
 * 9 || 3150 || 270 || 1375 || 700 ||
 * 10 || 3500 || 300 || 1500 || 700 ||

**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 customer increases 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 || 1010 ||
 * 3 || 1050 || 90 || 375 || 700 || 1165 ||
 * 4 || 1400 || 120 || 500 || 700 || 1320 ||
 * 5 || 1750 || 150 || 625 || 700 || 1475 ||
 * 6 || 2100 || 180 || 750 || 700 || 1630 ||
 * 7 || 2450 || 210 || 875 || 700 || 1785 ||
 * 8 || 2800 || 240 || 1000 || 700 || 1940 ||
 * 9 || 3150 || 270 || 1125 || 700 || 2095 ||
 * 10 || 3500 || 300 || 1250 || 700 || 2250 ||

Van rental is always constant because one van supposing can hold 10 customers so the formula would be 700+$155c, where c stands for the number of customers and 155 is the cost for bike rental and food and camp costs which each customer has to pay. To work this formula you would have to multiply 155 with a certain number of customers and then add 700 and you would get the total cost.


 * 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 || 1010 || - 310 ||
 * 3 || 1050 || 90 || 375 || 700 || 1165 || - 115 ||
 * 4 || 1400 || 120 || 500 || 700 || 1320 || 80 ||
 * 5 || 1750 || 150 || 625 || 700 || 1475 || 275 ||
 * 6 || 2100 || 180 || 750 || 700 || 1630 || 470 ||
 * 7 || 2450 || 210 || 875 || 700 || 1785 || 665 ||
 * 8 || 2800 || 240 || 1000 || 700 || 1940 || 860 ||
 * 9 || 3150 || 270 || 1125 || 700 || 2095 || 1055 ||
 * 10 || 3500 || 300 || 1250 || 700 || 2250 || 1250 ||

With a trip with 5 customers you would earn $275, with 10 customers you would earn $1250 with 25 you would earn about $4175.

__** Problem 3.4 Follow Up **__ **1) What other patterns of change do you see in the table?** The bike rental is always increasing by 30, the food and camp costs increase by 125, van rental is constant 700, and total cost increases by 155 per customer.  **2) What is the least number of customers needed for the tour to make a profit?** The least number of customers needed to make a profit is 4 customers. **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 think the least number should be around 10 because with more student you are saving more money. Also because with that amount they could start a small bike tour shop/business and buy their own bikes and have no bike rental costs.