College Algebra Math 130 Amy Jones Lewis

Warm-Up  Solve for the unknown  k = 27  ¼m = 195  7t + 25 = 4

Moving a Sand Pile

You are a materials handler for a large sand and concrete company. This means that you must monitor all orders for sand, gravel, and concrete coming into and going out of the company’s storage yard. Because of the large amount of material that is being moved, the storage yard is located next to a river and the material is moved on the river by barges.

Moving a Sand Pile There is an enormous pile of sand, estimated to be 2500 cubic feet, which must be loaded onto a barge on the river. You have a bucket loader to transfer the sand to the barge. The bucket loader can pick up five cubic feet of sand in its bucket.

Moving a Sand Pile  Find the amount of sand left in the pile after the bucket loader has transferred:  50 buckets to the barge.  200 buckets to the barge.  400 buckets to the barge.  600 buckets to the barge.  Use a complete sentence to explain how you found your answers.

Moving a Sand Pile  You can represent the amount of sand left in the pile using the variable p and the number of buckets of sand removed from the pile using the variable b.  Write an equation that represents the amount of sand left in the pile in terms of the number of buckets of sand that are removed.

Moving a Sand Pile  Find the number of buckets of sand that were removed from the pile if  2000 cubic feet of sand remain in the pile.  1550 cubic feet of sand remain in the pile.  100 cubic feet of sand remain in the pile.  3000 cubic feet of sand remain in the pile.  No sand remains in the pile.  Use a complete sentence to explain how you found your answers.

Moving a Sand Pile  Create a table of values that describes the relationship between the amount of sand in the pile and the number of buckets of sand removed.

Moving a Sand Pile  How does the amount of sand left in the pile change as the number of buckets of sand increases by one bucket?  How does the amount of sand left in the pile change as the number of buckets of sand increases by five buckets?  How does the amount of sand left in the pile change as the number of buckets of sand increases by one hundred buckets?

Moving a Sand Pile  Create a graph of the data from the table. Be sure to start by choosing your bounds and intervals. Label your graph clearly.

 Use your graph to find the number of buckets of sand that were removed from the pile if:  1000 cubic feet of sand remain.  500 cubic feet of sand remain.  2200 cubic feet of sand remain.  Use your graph to find the amount of sand left in the pile if:  100 buckets of sand were removed.  250 buckets of sand were removed.  350 buckets of sand were removed. Moving a Sand Pile

 Write ordered pairs given by the values in your table.  The ordered pairs that you wrote form a relation. A relation is any set of ordered pairs. The first coordinate of an ordered pair in a relation is the input and the second coordinate is the output.  Identify the inputs and outputs of the relation given by the ordered pairs that you wrote for this problem.

Moving a Sand Pile  A relation is a function if for each input there is exactly one output.  Determine whether the relation below is a function.  (2, 6), (3, 9), (4, 12), (5, 15), (6, 18)  (3, 3), (4, 1), (4, 6), (5, 0), (7, 5)  (1, 2), (2, 3), (3, 0), (4, 1), (5, 0)  The set of all input values of a function is the domain of the function, and the set of all output values is the range of the function.

Solving Equations  300 – 5f = 725  t = 9  10 = 14 – 2t

Homework  Relations & Functions  Next Class: Thursday, September 30th