Algebra Active Practice

1.The length of a rectangle is 5x+3. The width is 2x – 3. What is the area of the rectangle in terms of x?

2.The area of a rectangle is . The area of smaller rectangle is . What is the difference in their areas in terms of x?

3.The length of a rectangle is 3 more than twice its width. What is the area of the rectangle in terms of x?

4.The width of a rectangle is (x – 2) and the length is (x + 6). The area is 48. Write and solve an equation to determine the dimensions of the rectangle.

Answers:

1.

2.

3.

4.the rectangle is 4 by 12

Active Practice - Word problems for systems of equations

Remember to define x and y first, then write the two equations. Be sure to label the equations for what they represent.

  1. At a high school championship basketball game 1200 tickets were sold. Student tickets cost $1.50 each and adult tickets cost $5.00 each. The total revenue collected for the game was $3,200. How many students tickets were sold? How many adult tickets were sold?
  1. A small town is hosting a play as a fundraising project for a family in the town. Individuals may purchase tickets for $26 each. As a special incentive to attract couples, individuals may purchase a “couple package” for $32. (Note: The “couple package” allows 2 people to attend the play for the price of $32.) One the first day of sales, 23 tickets were sold and $694 was collected. How many tickets were sold to individuals for $26 each? How many people were convinced to buy the “couple package”?
  1. The treasurer of the student body at a college reported that the receipts from a recent concert totaled $916. Furthermore, he announced that 560 people had attended the concert. Students were charged $1.25 each for admission to the concert, and adults were charged $2.25 each. How many adults attended the concert? How many students attended the concert?
  1. Five hundred tickets were sold for a Saturday evening performance of a play. The tickets cost $7.50 for adults and $4.00 for students. A total of $3,312.50 was received for all the tickets sold that Saturday evening. How many adults attended the play? How many students attended the play?

Answers:

1.800 students and 400 adults tickets were sold

2.7 single tickets and 16 couple tickets were sold

3.486 adults attended and 430 students attended the concert

4.375 adults and 125 students attended the play

Algebra Active Practice

Quadratic formula – simplify radicand

Use the quadratic formula to solve for x. Leave your answer in simplified form.

1.

2.

Solve the quadratic by completing the square. Leave your answer in simplified form.

3.

4.

Solve the quadratic by factoring.

5.

6.

Answers:

1.x =

2.x =

3.x =

4.x =

5.x = – 5,

6.x = – 4, 15