Linear Algebra System of Equations, Inequalities

For Problem #s 1 and 2, show a valid system of equations/inequalities that could be used to solve each problem. You will only receive credit for the system; you will not receive credit for the solution.
1. At the end of a day, a toll collector counts the number of nickels and quarters deposited at the exact change lane. There is a total of 54572 coins and a total of $12944.40 collected. Write a system of linear equations to model this situation.

2. Alex is packing books into boxes. Each box holds either 12 small books or 7 larger books. Alex cannot use more than 30 boxes; however, he must pack a minimum of 250 books. Write a system of linear inequalities to model this situation.

For Problem #s 3 and 4, solve by using any method demonstrated in class. Please show the system of equations you used, all work, and correct units. If using a TI83/84, show the window settings ( Xmin , Xmax ) and ( Ymin , Ymax ) and coordinates of the intersection point.
3. A person invests a total of $25000 in the stock market. Some of this was invested in precious metals commodities, which earned 9.5% simple interest per year, and the rest was invested in crude oil commodities, which earned 7.25% simple interest per year. If the total interest earned after one year is $2001.50, how much money was invested in each commodity?

4. A jeweler needs to mix two copper alloys. One alloy contains 17% copper, and a second alloy contains 54% copper. How many ounces of each alloy must be mixed to obtain 48 ounces of another alloy that is 29% copper? (Please round all answers to the nearest hundredth.)

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