1) Define your variables, write a system of equations, use your calculator to solve the system of equations and answer the problem.The treasurer of the Spay and Neuter Clinic invested $8,000 of their savings into three different accounts, at annual rates of 4%, 5% and 6%. The total interest earned for the year was $410. The amount earned by the 6% account was $30 more than that earned by the 5% account. How much was invested at each rate?

amount invested in the 4% account.....$

amount invested in the 5% account.....$

amount invested in the 6% account......$

2) Write a system of linear equations that defines the verbal problem, and then answer the question. Three sides of a rectangular garden are enclosed by1000feetof fencing. The fourth side is next to a barn and requires no fencing. The length of the side of the garden that is parallel to the barn is100feetless than twice the width of the garden. What is the area of the rectangular garden?

3) Solve the system of three linear equations by the method of elimination

x + 2y + z = 24

3y - 3z =36

y - z =12

(x,y,z) = ( ________________)

4) Use partial fraction decomposition to solve for constants A and B:

2x + 1 = A + ___B

x^2 - x - 20 x + 4 x - 5

A=_____________

B=_____________

5) A grocer sells milk chocolate at $2.70 per pound, dark chocolate at $4.90 per pound, and dark chocolate with almonds at $5.80 per pound. He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.91 per pound. The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. How many pounds of each type must he use in this mixture?

amount of milk chocolate _____________ lbs

amount of dark chocolate______________ lbs

amount of dark chocolate with almonds_____________ lbs