Problem Solving

The Steps Understand the problem. Devise a plan to solve the problem. Carry out the plan. Look back.

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.

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

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?

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

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.

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)

Example Solve: Use the plan to answer the question. c = (94 × 5) + (141 × 2.25) c = $787.25

Example Check: Is your answer reasonable? Use estimation to check the answer. (90 × 5) + (150 × 2) = 450 + 300 = 750 The answer is reasonable.

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?

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.

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 $16.25. How much change did she receive from a $50 bill?

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?

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?

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?

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 $16.59. How much change did he receive after paying with a $20 bill and a $10 bill?

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?

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.

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?

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

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?