standard_description: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
problem_activity: Problem 1
A clothing manufacturer has to use at least 1,000 yards of cotton to make room for new inventory to make shirts and pajamas. A shirt requires 1 yard of fabric, and a pair of pajamas requires 3 yards of fabric. It takes 2 hours to make a shirt and 3 hours to make a pair of pajamas, and there are 1600 hours available to make all of the clothing. Let
$$x$$
represent the number of shirts and
$$y$$
represent the number of pajamas.
What is the smallest number of pajamas the manufacturer can make and meet all of these conditions?
Problem 2
Phil and Cath make and sell boomerangs for a school event. The money they raise will go to charity. They plan to make them in two sizes: small and large.
Phil will carve them from wood.
The small boomerang takes 2 hours to carve, and the large one takes 3 hours to carve.
Phil has a total of 24 hours available for carving.
Cath will decorate them. She only has time to decorate 10 boomerangs of either size.
Phil and Cath want to make as much money for charity as they can.
The small boomerang will make $8 for charity.
The large boomerang will make $10 for charity.
How many small and large boomerangs should they make?
How much money will they then make?


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