Name
Class
Date
4-1 • Guided Problem Solving
GPS
Student Page 130, Exercise 27:
Cooking To make pancakes, you need 2 cups of water for every
3 cups of flour. Write an equivalent ratio to find how much water you
will need with 9 cups of flour.
Understand
1. Circle the information you will need to solve.
All rights reserved.
2. What are you being asked to do?
3. Why will a ratio help you to solve the problem?
4. What is the ratio of the cups of water
to the cups of flour?
5. How many cups of flour are you using?
6. Write an equivalent ratio to use 9 cups
of flour. 7. How many cups of water are
needed for 9 cups of flour?
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Plan and Carry Out
Check
8. Why is the number of cups of water triple the number of cups
needed for 3 cups of flour?
Solve Another Problem
9. Rebecca is laying tile in her bathroom. She needs 4 black tiles for
every 16 white tiles. How many black tiles are needed if she uses
128 white tiles?
162
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Course 2 Lesson 4-1
Guided Problem Solving
10/10/12 1:32 PM
Name
Class
Date
4-2 • Guided Problem Solving
GPS
Student Page 135, Exercise 27a:
Geography Population density is the number of people per unit of
area. Alaska has the lowest population density of any state in the
United States. It has 626,932 people in 570,374 mi2. What is its
population density? Round to the nearest person per square mile.
Understand
All rights reserved.
1. What is population density?
2. What are you being asked to do?
3. What does the phrase people per unit of area imply?
4. What is the population of Alaska?
5. What is the area of Alaska?
6. Write a division expression for
the population density.
7. What is its population density?
8. Round to the nearest person
per square mile.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Plan and Carry Out
Check
9. Why is the population density only about 1 person/mi2?
Solve Another Problem
10. Mr. Boyle is buying pizza for the percussion band. The bill is
$56.82 for 5 pizzas. If there are 12 members of the band, how
much does the pizza cost per member? Round to the nearest cent.
164
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Course 2 Lesson 4-2
Guided Problem Solving
10/10/12 1:32 PM
Name
Class
Date
4-3 • Guided Problem Solving
GPS
Student Page 139, Exercise 29:
Decorating A certain shade of green paint requires 4 parts blue to
5 parts yellow. If you mix 16 quarts of blue paint with 25 quarts of yellow paint,
will you get the desired shade of green? Explain.
Understand
1. Circle the information you will need to solve.
All rights reserved.
2. What are you being asked to do?
3. Will a ratio help you to solve the problem? Explain.
Plan and Carry Out
4. What is the ratio of blue parts to yellow parts?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. What is the ratio of blue quarts to yellow quarts? 6. Check to see if the cross products of the two ratios are equal.
7. Are the ratios the same? 8. Will you get the desired shade of green? Explain.
Check
9. How do you know that the ratios are not the same?
Solve Another Problem
10. There are 15 boys and 12 girls in your math class. There are 5 boys
and 3 girls in your study group. Determine if the boy to girl ratio
is the same in study group as it is in your math class. Explain.
166
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Course 2 Lesson 4-3
Guided Problem Solving
10/10/12 1:32 PM
Name
Class
Date
4-4 • Guided Problem Solving
GPS
Student Page 146, Exercise 28:
There are 450 students and 15 teachers in a school. The school hires
2 new teachers. To keep the student-to-teacher ratio the same, how
many students in all should attend the school?
Understand
1. What are you being asked to do?
All rights reserved.
2. Will a proportion help you to solve the problem? Explain.
Plan and Carry Out
3. Write a ratio for the current student-to-teacher ratio.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4. Write a ratio for the new student-to-teacher ratio.
5. Write a proportion using the ratios in Steps 3 and 4.
6. How many total students should attend the school?
Check
7. Are the two ratios equivalent? Explain.
Solve Another Problem
8. There are 6 black marbles and 4 red marbles in a jar. If you add
4 red marbles to the jar, how many black marbles do you need to
add to keep the ratio of black marbles to red marbles the same?
168
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Course 2 Lesson 4-4
Guided Problem Solving
10/10/12 1:32 PM
Name
Class
Date
4-5 • Guided Problem Solving
GPS
Student Page 153, Exercise 13:
Geometry A rectangle with an area of 32 in2 has one side measuring
4 in. A similar rectangle has an area of 288 in2. How long is the
longer side in the larger rectangle?
Understand
1. What are you being asked to do?
All rights reserved.
2. Will a proportion that equates the ratio of the areas to the ratio
of the shorter sides result in the desired answer? Explain.
3. What measure should you determine first?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Plan and Carry Out
4. What is the length of the longer side of the rectangle
whose area is 32 in.2 and whose shorter side is 4 in.? 5. What is the ratio of the longer side to the shorter side? 6. What pairs of factors multiply to equal 288?
7. Which pair of factors has a ratio of 2 ? 1
8. What is the length of the longer side? Check
9. Why must the ratio between the factors be 2 ?
1
Solve Another Problem
10. A triangle with perimeter 26 in. has two sides that
are 8 in. long. What is the length of the third side of
a similar triangle which has two sides that are 12 in. long? 170
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Course 2 Lesson 4-5
Guided Problem Solving
10/10/12 1:33 PM
Name
Class
Date
4-6 • Guided Problem Solving
GPS
Student Page 161, Exercise 23:
Writing in Math You are making a scale drawing with a scale of
2 in. 5 17 ft. Explain how you find the length of the drawing of an
object that has an actual length of 51 ft.
Understand
1. What are you being asked to do?
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2. What points should you include in your explanation?
3. What is a scale?
Plan and Carry Out
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4. What is the scale? 5. What is the actual length of the object? 6. Write a proportion using the scale, the actual
length, and the unknown length of the drawing. 7. What is the length of the object in a drawing? Check
8. Use Steps 4–7 to explain how you decided how long to draw the
object.
Solve Another Problem
9. The length of the wing of a model airplane is 3 in.
If the scale of the model to the actual plane is
1 in. 5 25 ft, what is the length of the actual wing? 172
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Course 2 Lesson 4-6
Guided Problem Solving
10/10/12 1:33 PM
Name
Class
Date
4-7 • Guided Problem Solving
GPS
Student Page 168, Exercise 15:
Error Analysis A salesperson showed the table below while
explaining that oranges are the same price per pound, no matter
what size bag they come in. Why is the salesperson wrong?
$
$8
$10
$20
lbs
4
6
10
All rights reserved.
Understand
1. What are you being asked to do?
2. What will you use to find the answer?
Plan and Carry Out
4. What is the unit price for 6 pounds of oranges? 5. What is the unit price for 10 pounds of oranges? 6. Why is the salesperson wrong?
Check
7. How can you check your answer?
Solve Another Problem
8. A customer thinks pizzas cost the same per slice at a local
restaurant. Why is the customer wrong?
$
$8
$9
$12
Slices
10
12
16
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3. What is the unit price for 4 pounds of oranges? 174
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Course 2 Lesson 4-7
Guided Problem Solving
10/10/12 1:33 PM