Figuring out weighted averages

The Problem An Astrodollars Coffee shop sells several different types of whole coffee beans. Last Monday they sold 100 pounds of Honduran coffee beans, 70 pounds of Guatemalan coffee beans, 40 pounds of Nicaraguan coffee beans, and 40 pounds of Chilean coffee beans. The Honduran beans cost 8 per pound, the Guatemalan beans cost 9 per pound, the Nicaraguan beans cost 10.50 per pound, and the Chilean beans cost 13.50 per pound. What was the average cost per pound of the coffee beans sold on Monday  

Set up a proportion where each poundage multiplies its respective price. Put the sum of all the products you get in the numerator of a fraction, and divide by the total number of pounds. That s one side of the proportion. Set that fraction equal to another fraction with a 1 in the denominator (opposite the total number of pounds) and an x in the numerator. 

Now simplify the proportion by doing the multiplications and additions then reduce the fraction on the left. Cross-multiply and solve for x, and you get 9.56 for the average cost of the coffee beans sold on Monday. 

The Problem Nick took five courses last semester and needs to determine his GPA. He got an A in his 4-semester-hour calculus course, an Ain his 1-semester-hour computer course, a B in his 5-semester-hour biology course, a C in his 3-semester-hour English course, and a B in his 3-semester-hour Spanish course. What is his GPA for the semester  

Multiply each number of semester hours by its worth in terms of points for that grade, and add up all the points divide by the total number of semester hours. Set that fraction equal to x divided by 1. 

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