problem solving. 1.understand the problem. 2.devise a plan to solve the problem. 3.carry out the...

Problem SolvingProblem Solving

1. Understand the problem.

2. Devise a plan to solve the problem.

3. Carry out the plan.

4. Look back.

The StepsThe Steps

1. Read to understand the question and identify the needed data.

2. Plan what to do to solve the problem.

3. Solve the problem by carrying out the plan.

Four Point ChecklistFour Point Checklist

4. Check to make sure the solution is reasonable.

Four Point ChecklistFour Point Checklist

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?

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?

ExampleExample

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

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

ExampleExample

1. Read1. ReadQuestion: 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.

ExampleExample

2. Plan: Determine how the given information relates to what you are trying to find.

2. Plan: Determine how the given information relates to what you are trying to find.

ExampleExample

Let c be the total cost.c = (number of adult tickets ×

cost per ticket) + (number of child tickets × cost per ticket)

3. Solve: Use the plan to answer the question.

3. Solve: Use the plan to answer the question.

ExampleExample

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

4. Check: Is your answer reasonable? Use estimation to check the answer.

4. Check: Is your answer reasonable? Use estimation to check the answer.

ExampleExample

(90 × 5) + (150 × 2) = 450 + 300 = 750

The answer is reasonable.

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?

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?

ExampleExample

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.

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.

ExampleExample

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?

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?

ExerciseExercise

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?

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?

ExerciseExercise

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?

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?

ExerciseExercise

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?

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?

ExerciseExercise

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?

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?

ExerciseExercise

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?

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?

ExerciseExercise

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.

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.

ExerciseExercise

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?

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?

ExerciseExercise

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

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

ExerciseExercise

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?

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?

ExerciseExercise