Name: Class: Date: ID: A

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1 Class: Date: Chapter Essentail Skills REVIEW 1. The Sharks Aquatic Club recently held a fundraiser to raise money for a local charity. The swimmers received money for each lap that they swam during a one-week period. The three swimmers who raised the most money were Rita, John, and Rodell. Together they swam a total of 2125 laps. John swam three times as many laps as Rita, and Rodell swam 25 more laps than John. How many laps did each swimmer swim? a. Draw a picture to represent the situation. Rita: John: Rodell: b. Determine the number of laps each person swam using the picture you created. Explain your reasoning or show your work. Rita: John: Rodell: c. Write an expression for the number of laps each person swam. Let L represent the number of laps swum by Rita. The number of laps swum by Rita: The number of laps swum by John: The number of laps swum by Rodell: d. Write an equation to represent this situation. e. If the swimmers received $2 for every lap they swam, how much did each swimmer earn for charity? 1

2 2. Two friends pooled the tickets they won from playing video games to get a prize that requires 500 tickets. If friend A won 80 more tickets than friend B, how many tickets did each friend win? c. Determine the number collected by each person using the picture. Explain your Friend A : Friend B : 3. Lamar, Harris, and Tyler ran a 22 -mile relay race as a team. Tyler ran 2 miles farther than Harris, and Lamar ran twice as far as Harris. How many miles was each boy s leg of the race? c. Determine the distance run by each person using the picture. Explain your Lamar : Harris : Tyler: 4. The Petersons set aside $1000 to donate to their three favorite charities: the children s home, the food bank, and the animal shelter. They gave twice as much to the food bank as to the animal shelter. Their donation to the children s home was $100 more than the donation to the food bank. How much did each charity receive from the Petersons? c. Determine the amount each charity recieved using the picture. Explain your Children s Home: Food Bank : Animal Shelter: 2

3 5. Madison Middle School has a Math and Science Club that holds meetings after school. The club has decided to enter a two-day competition that involves different math and science challenges. The first day of competition involves solving multi-step math problems. Teams will receive one point for every problem they get correct. Halfway through the day, the Madison Middle School Team has 4 points. After a dinner break, the team does more problems and is able to finish the day with 11 points. a. The representation shows a balance for this situation. The left side of the balance represents the 4 points the team had at midday plus the additional points they got after dinner. The right side of the balance represents the total points they had at the end of the day. What will balance 1 rectangle in this representation? Describe your strategy. Strategy: What will balance 1 rectangle? = b. Rewrite the representation from part (a) using symbols. Let = x and = 1 point. Then describe how the strategies you used to determine what balanced 1 rectangle can apply to the equation. algebraic equation: Strategies: c. Does your answer for x maintain balance in the original equation? Substitute the value of x back into the original equation to check. Show your work. d. What does the value x = 7 mean in the original situation? make sure to label 3

4 6. The second day of a math and science competition involves all hands-on science problems. Because of the complexity of the problems, each team will get 3 points for every science problem that they get correct. The Madison Middle School team is starting the day with 11 points. By the end of the day the team had 23 points. a. The representation shows a balance for this situation. The left side of the balance represents the 11 points the team had at the start of the day plus the additional points they got from the science competition. The right side of the balance represents the total points they had at the end of the second day. What will balance 1 rectangle in this representation? Describe your strategy. = Strategy: b. Rewrite the representation from part (a) using symbols. Let = x and = 1 point. Then describe how the strategies you used to determine what balanced 1 rectangle can apply to the equation. algebraic equation: Strategies: c. Does your answer for x maintain balance in the original equation? Substitute the value of x back into the original equation to check. Show your work. Determine what will balance one rectangle. Explain your solution. Then rewrite each representation as an equation. 7. 4

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