Name



Name __________________________________ Date ___________________

LESSONS 2.1-2.4

Problem Solving: Mixed Problem Solving

1. Multi-Step Problem The table below shows the number of bacteria after each hour for 5 hours.

|Hour |Billions of bacteria |

|0 |3 |

|1 |6 |

|2 |12 |

|3 |24 |

|4 |48 |

|5 |96 |

a. Describe the pattern, if any, in the times shown in the table.

b. Use the data in the table to make a reasonable prediction of the amount of bacteria after 8 hours.

2. Extended Response The graph shows the sales of MP3 players sold at 5 different prices. Tell whether each statement is the result of inductive reasoning or deductive reasoning. Explain your reasoning.

[pic]

a. If the price is set at $190, the company can expect sales around 22,000.

b. The sales were lowest at a price of $250.

c. If the price is set at $275, then the company can expect sales of 4000.

3. Open-Ended Create a conditional statement. Then, write the converse, inverse, and contrapositive of the conditional statement.

4. Short Response Select the phrase or word that makes the conclusion true. Explain your reasoning.

a. The Pine Meadows apartment building does not allow dogs. Adam lives at Pine Meadows. So, Adam (must, may, or may not) keep a dog.

b. Zion National Park is in Utah. Jodi spent a week in Utah. So, Jodi (must have, may have, or never) visited Zion National Park.

5. Gridded Answer Write the next number in the pattern.

1, 3, 7, 13, 21, 31,...

6. Short Response The table below shows the magnitude given to earthquakes and their effects. Use the table to determine whether the statement is true or false. If false, provide a counterexample.

|Richter Magnitude |Earthquake Effects |

|less than 3.5 |generally not felt, but recorded |

|3.5-5.4 |often felt, rarely causes damage |

|5.5–6.0 |Slight damage to buildings |

|6.1–6.9 |Destructive where people live |

|7.0–7.9 |Major, causes serious damage |

|8.0 or greater |Great earthquake, great destruction |

a. An earthquake is a great earthquake if and only if its Richter magnitude is 8.0 or greater.

b. An earthquake is often felt if and only if its Richter magnitude is 3.5.

Name __________________________________ Date ___________________

LESSONS 2.4 & 2.7

Problem Solving Workshop: Gridded Answer Sheet

For use with Mixed Problem Solving for 2.1–2.4 and 2.5–2.7

Name __________________________________ Date ___________________

LESSON 2.5

Problem Solving Workshop: Worked Out Example

PROBLEM

Body Weight The ideal male body weight w (in pounds) can be determined from a man’s height h (in inches) using the formula w = 5(h – 60) + 110. Solve the formula for h and write a reason for each step.

STEP 1

Read and Understand

What do you know?

The equation for ideal male body weight as a function of height.

What do you want to find out?

The height of a male using ideal male body weight.

STEP 2

Make a Plan Use what you know to solve the problem.

STEP 3

Solve the Problem Use the Distributive Property to solve the problem.

|Equation |Explanation |Reason |

|w = 5(h – 60) +110 |Write original equation. |Given |

|w = 5h – 190 |Multiply, then add. |Distributive Property |

|w + 190 = 5h |Add 190 to each side. |Addition Property of |

| | |Equality |

| |Divide each side by 5. |Division Property of |

| | |Equality |

STEP 4

Look Back You can also solve the problem another way.

|w = 5(h – 60) +110 |Write original equation. |

|w – 110 = 5(h – 60) |Subtract 110 from each side. |

| |Divide each side by 5. |

| |Add to each side. |

PRACTICE

1. Wind-Chill Factor If the wind is blowing at 20 miles per hour, you can find the temperature T (in degrees Fahrenheit) by using the equation

where W is the

wind-chill temperature (in degrees Fahrenheit). Solve the equation for W and write a reason for each step. What is the wind-chill temperature if the actual temperature is 18°F and the wind is blowing at 20 miles per hour?

2. Body Weight The ideal female body weight w (in pounds) can be determined from a woman’s height h (in inches) using the formula w = 5(h – 60) + 100. Solve the formula for h and write a reason for each step. Find the height of a woman with an ideal weight of 110 pounds.

Name __________________________________ Date ___________________

LESSONS 2.5–2.7

Problem Solving: Mixed Problem Solving

1. Multi-Step Problem In the diagram below, m(YWX = m(YWZ.

a. Prove m(XWZ = 2(m(YWX).

b. If m(XWZ = 56(, what is m(YWZ?

2. Multi-Step Problem The distance from the electronics store to the supermarket is the same as the distance from the gas station to the car wash. The distance from the hardware store to the electronics store is the same as the distance from the supermarket to the diner, and from the diner to the gas station.

Use the steps below to prove that the distance from the hardware store to the diner is the same as the distance from the supermarket to the car wash.

a. Draw and label a diagram to show the mathematical relationships.

b. State what is given and what is to be proved for the situation.

c. Write a two-column proof.

3. Open-Ended In the diagram below, m(LMK = 70° and bisects m(LMN. Give two more true statements about the diagram.

4. Gridded Answer The foul lines of a baseball field intersect at home plate to form a right angle. Suppose you hit a baseball whose path is between the foul lines and forms an angle of 22° with the first base foul line. Find the measure of the angle between the third base foul line and the path of the baseball in degrees.

5. Short Response In auto racing, the turns are banked, which helps the cars travel around the track at high speeds because the angles provide an inward force that helps keep the cars from flying off the track. The Daytona International Speedway in Florida has four banked turns. Use the information given below to find m(3. Explain your steps.

m(1 + m(3 + m(4 = 93(

m(2 + m(4 =62°

m(2 = m(3

m(1 = m(2

6. Extended Response A formula you can use to calculate your new wage after a pay raise is W = c(l + r) where W is your new wage (in dollars per hour), c is your current wage (in dollars per hour), and r is your percent increase written as a decimal.

a. Solve the formula for r. Give a reason for each step

b. Use the formula from part (a) to find your percent increase if your current wage is $10 and you new wage will be $l0.80.

c. Suppose Donald gets a 6% raise and his new wage is $12.72. Find Donald’s old wage. Explain the steps you used to find your answer.

d. Look back at the steps you used to solve the formula for r. Could you have solved for r in a different way? Explain.

Name __________________________________ Date ___________________

LESSONS 2.4 & 2.7

Problem Solving Workshop: Gridded Answer Sheet

For use with Mixed Problem Solving for 2.1–2.4 and 2.5–2.7

-----------------------

w

h

+ð

=ð

110

5

w

h

-ð

=ð

-ð

110

60

5

w

h

+ð

=ð

190

5

300

5

(

)

T

W

=ð

+ð

(

)

50

71

77

2

JK

+

’

110

5

w

h

−

’

−

110

60

5

w

h

+

’

190

5

300

5

(

)

T

W

’

+

(

)

50

71

77

2

JK

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