1. The perimeter of a standard-sized rectangular rug is 32 ft. The length is 2 ft greater than the width. Find the dimensions using the following system.
2 + w = ℓ
2w + 2ℓ = 32
2. A rental company charges $42.00 a day plus $0.36 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y = 0.36x + 42. A second company charges $34.00 a day plus $0.46 per mile, so the daily cost, y, if x miles are driven is described by y = 0.46x + 34. The graphs of the two equations are shown in the same rectangular coordinate system.
a. Determine from the graph the x-coordinate of the intersection point of the two graphs.
b. Describe what this x-coordinate means in practical terms. Choose the correct answer below.
A. The maximum amount of miles that can be driven is 80.
B. The maximum amount that both companies charge is $80.
C. Both companies charge $80 for the same number of miles driven.
D. Both companies charge the same for 80 miles driven.
c. Substitute the x-coordinate of the intersection point from part (a) into one of the two equations. Find the corresponding value for y.
d. Describe what this value represents in practical terms. Choose the correct answer below.
A. Both companies charge $70.80 for 70 miles driven.
B. Both companies always charge more than $70.80.
C. Both companies charge $70.80 for 80 miles driven.
D. Both companies always charge less than $70.80.
3. A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,300 ft. Determine the flag's width and length if the length is 410 ft greater than the width.
4. You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $30.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $5.00 with a charge of $0.10 per minute for all long-distance calls.
a. For how many minutes of long-distance calls will the costs for the two plans be the same? What will be the cost for each plan?
b. If you make approximately 10 long-distance calls per month, each averaging 30 minutes, which plan should you select?
5. Over a season in a women's basketball league Jackie scored 42 more points than the second-highest scorer, Leslie. Together, Jackie and Leslie scored 1210 points during the season. How many points did each player score over the course of the season?
6. Find the measures of two complimentary angles if one angle is 10° more than three times the other angle.
a. The smaller angle measures °.
b. The larger angle measures °.