Prepping for the Robot Challenge Solving Linear Systems Graphically and Algebraically

Transcription

1 LESSON.1 Skills Practice Name Date Prepping for the Robot Challenge Solving Linear Sstems Graphicall and Algebraicall Vocabular Match each term to its corresponding definition. 1. a process of solving a sstem of equations b substituting a variable in one equation with an equivalent expression a. sstem of linear equations 2. sstems with no solutions b. break-even point 3. the point when the cost and the income are equal c. substitution method 4. sstems with one or man solutions d. consistent sstems 5. two or more linear equations that define a relationship between quantities e. inconsistent sstems Chapter Skills Practice 421

2 LESSON.1 Skills Practice page 2 Problem Set Write a sstem of linear equations to represent each problem situation. Define each variable. Then, graph the sstem of equations and estimate the break-even point. Explain what the break-even point represents with respect to the given problem situation. 1. Eric sells model cars from a booth at a local flea market. He purchases each model car from a distributor for $12, and the flea market charges him a booth fee of $50. Eric sells each model car for $20. Eric s income can be modeled b the equation 5 20x, where represents the income (in dollars) and x represents the number of model cars he sells. Eric s expenses can be modeled b the equation 5 12x 1 50, where represents the expenses (in dollars) and x represents the number of model cars he purchases from the distributor x 5 12x x Number of Model Cars Income Expenses The break-even point is between and 7 model cars. Eric must sell more than model cars to make a profit. 422 Chapter Skills Practice 809_Skills_Ch0.indd 422 4/23/12 12:05 PM

3 LESSON.1 Skills Practice page 3 Name Date 2. Ramona sets up a lemonade stand in front of her house. Each cup of lemonade costs Ramona $0.30 to make, and she spends $ on the advertising signs she puts up around her neighborhood. She sells each cup of lemonade for $ x Cups of Lemonade Chapter Skills Practice 423

4 LESSON.1 Skills Practice page 4 3. Chen starts his own lawn mowing business. He initiall spends $180 on a new lawnmower. For each ard he mows, he receives $20 and spends $4 on gas x Number of Yards Mowed 424 Chapter Skills Practice 809_Skills_Ch0.indd 424 4/23/12 12:05 PM

5 LESSON.1 Skills Practice page 5 Name Date 4. Olivia is building birdhouses to raise mone for a trip to Hawaii. She spends a total of $30 on the tools needed to build the houses. The material to build each birdhouse costs $3.25. Olivia sells each birdhouse for $ x Number of Birdhouses Chapter Skills Practice 425

6 LESSON.1 Skills Practice page 5. The Spanish Club is selling boxes of fruit as a fundraiser. The fruit compan charges the Spanish Club $7.50 for each box of fruit and a shipping and handling fee of $100 for the entire order. The Spanish Club sells each box of fruit for $ x Number of Fruit Boxes 42 Chapter Skills Practice 809_Skills_Ch0.indd 42 4/23/12 12:05 PM

7 LESSON.1 Skills Practice page 7 Name Date. Jerome sells flowers for $12 per bouquet through his Internet flower site. Each bouquet costs him $5.70 to make. Jerome also paid a one-time fee of $150 for an Internet marketing firm to advertise his compan x Number of Bouquets Chapter Skills Practice 427

8 LESSON.1 Skills Practice page 8 Transform both equations in each sstem of equations so that each coefficient is an integer x x x x x ) 3 ( x ) x x ( x x x x x x x x x x Chapter Skills Practice 809_Skills_Ch0.indd 428 4/23/12 12:05 PM

9 LESSON.1 Skills Practice page 9 Name Date Solve each sstem of equations b substitution. Determine whether the sstem is consistent or inconsistent x 2 3 x (4) The solution is (4, 5). The sstem is consistent x x x x x x Chapter Skills Practice 429

10 LESSON.1 Skills Practice page x x x x Chapter Skills Practice 809_Skills_Ch0.indd 430 4/23/12 12:05 PM