algebra mid-term

1) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

2) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

3) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

4) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

5) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

6) The area of an oil spill on land varies directly as the volume of oil spilled. If an 80-gallon oil spill covers an area of 180 square feet, how many square feet would a 200-gallon oil spill cover?

Please include the following in your work:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

7) In kick boxing, the energy needed to break a board of standard width and thickness varies inversely with the length of the board. If 3.2 Joules of energy are required to break an 27-inch board, how many Joules of energy are required to break a 24-inch board?

Please include the following in your work:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

8) A plumber cut a 40-foot piece of pipe into two pieces. The length of the longer piece was eight feet more than three times the length of the shorter piece. What was the length of each piece of pipe?

Please include the following in your work:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

9) Bob left Andrew’s house and drove toward the ocean. One hour later, Andrew left, driving 12 mph faster than Bob in an effort to catch up with him. After three hours, Andrew caught up with Bob. What was each man’s average rate?

Please include the following in your work:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

10) Becky would like to have at least $240,000 saved for her daughter’s college education. If she invests $95,000 in an education account paying 6.15% interest compounded quarterly, will she reach her goal in 18 years? Show all work to justify your answer and include appropriate units. The final amount in the account should be rounded to the nearest cent.

Please include the following in your work:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

759

5

42

yy

=-

1235

1

2123

yy

-=+

(

)

73248

xx

-=-

(

)

(

)

153331436

yyy

-=+–

(

)

(

)

382842

xxx

+=–

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