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## Symbolic Representation

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**Symbolic Representation**Section 0.2**Example A**When Adam and his sister Megan arrive at a party, they see that there is 1 adult chaperone for every 4 kids. Right behind them come 30 more boys, and Megan notices that the ratio is now 2 boys to 1 girl. However, behind the 30 boys come 30 more girls, and Adam notices that there are now 4 girls for every 3 boys. What is the final ratio of adult chaperones to kids?**Example B**Three friends went to the gym to work out. None of the friends would tell how much he or she could leg-press, but each hinted at their friends’ leg-press amounts. ● Chen said that Juanita and Lou averaged 87 pounds. ● Juanita said that Chen leg-pressed 6 pounds more than Lou. ● Lou said that eight times Juanita’s amount equals seven times Chen’s amount. Find how much each friend could leg-press.**Select one of the problems below, and use these four steps**to find a solution. • Step 1 List the unknown quantities, and assign a variable to each quantity. • Step 2 Write one or more equations that relate the unknown quantities to conditions of the problem. • Step 3 Solve the equations to find a value for each variable. • Step 4 Interpret your solution according to the context of the problem. • When you finish, write a paragraph answering this question: Which of the four problem-solving steps was hardest for you? Why?**Problem 1**• On Monday the manager scheduled two clerks and one supervisor for 8-hour shifts. • She was pleased because she met the daily salary budget. • On Tuesday the manager needed two clerks for 8 hours, a third clerk for 4 hours, and one supervisor for 4 hours. She was very pleased to be $10 under budget. • On Wednesday she needed three clerks for 8 hours and one supervisor for 4 hours. This day she was over budget by $20. • All of the clerks make the same hourly wage. What is the daily salary budget?**Problem 2**• Sandy uses a ton pickup (a truck that can carry 1000 pounds) to transport ingredients for mortar. • Sand comes in 50-pound bags and cement comes in 40-pound bags. Mortar is made from five bags of sand for every bag of cement. • How many bags of each should Sandy load to make the most mortar possible?