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Problem Solving

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**The Steps Understand the problem. Devise a plan to solve the problem.**

Carry out the plan. Look back.

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Four Point Checklist Read to understand the question and identify the needed data. Plan what to do to solve the problem. Solve the problem by carrying out the plan.

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Four Point Checklist Check to make sure the solution is reasonable.

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Example Tickets for the school play cost $5 for adults and $2.25 for children. If 94 adults and 141 children attended the play, what was the total amount of ticket money collected?

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Example Read: Determine what the question is and identify the given information.

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**Example Read Question: How much money was collected for tickets?**

Information: Ticket prices were $5 for adults and $2.25 for children; 94 adults and 141 children attended.

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Example Plan: Determine how the given information relates to what you are trying to find. Let c be the total cost. c = (number of adult tickets × cost per ticket) + (number of child tickets × cost per ticket)

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**Example Solve: Use the plan to answer the question.**

c = (94 × 5) + (141 × 2.25) c = $787.25

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Example Check: Is your answer reasonable? Use estimation to check the answer. (90 × 5) + (150 × 2) = = 750 The answer is reasonable.

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Example Mrs. Jacobs bought 2 lb. of bananas for $0.68/lb., a box of wafer cookies for $2.68, and a box of vanilla pudding for $0.89. She paid with a $20 bill. How much change should she receive?

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Example The Robbins family is planning a vacation. They plan to drive 318 mi. the first day, 350 mi. the second day, and 225 mi. the third day. The cost of gasoline for their car is about $0.10 per mile. How much will their gas cost? Round to the nearest dollar.

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Exercise Amy bought a 10 lb. bag of potatoes for $4.29, 3 lb. of apples at $1.29/lb., and a honey-baked ham for $ How much change did she receive from a $50 bill?

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Exercise Whitewater Rentals has 39 canoes and 25 solo kayaks. The canoes rent for $45 for a six-hour trip. The solo kayaks rent for $49 for the same trip. One day 8 canoes and 4 kayaks were not rented. How much money was collected for rentals that day?

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Exercise Twenty–five men volunteered to lay 1,450 pieces of sod around a new church building. If each man was given an equal number of pieces, how many pieces did each man get?

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Exercise Karina purchased 5 yd. of fabric costing $7.99/yd., two spools of thread at $1.25/spool, and a pattern costing $5.75. What was the total amount of her purchase before tax?

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Exercise Dan bought a 5 lb. bag of sugar for $2.19, 2 lb. of apples at $1.09/lb., and a 20 lb. box of laundry detergent for $ How much change did he receive after paying with a $20 bill and a $10 bill?

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Exercise The eighth-grade class plans to produce a three-act play. The set for the play will cost $420, the play scripts will cost $250, and the costumes for the play will cost $175. What will be the total cost of the play?

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Exercise If the tickets for the play cost $3 and 350 people attend, what will be the total income from the play? Find the profit or loss for the class on this venture.

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Exercise The soccer team plans to take five trips to visit schools for games this season. The roundtrip mileage for the five trips is as follows: 44 mi., 126 mi., 60 mi., 188 mi., and 244 mi. What is the total mileage for the trips?

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Exercise If the school budgets $0.42/mi. for gasoline, what will be the total budgeted for the trips?

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Exercise Tri-City Rent-All has six mowers and three tillers that can each be rented for $29 per day. One day two mowers and one tiller were not rented. How much money was collected in rent for the machines that day?

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Chapter 1: Expressions, Equations, & Inequalities

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