Section 4 Problem Solving Strategies and Word Problems

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Chapter 4

• Section 4 Problem Solving Strategies and Word
  Problems

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Practice Writing Equations

• Worksheet

3
Practice Answer Key

• 1) The sum of a number and the number decreased
  by five is 25.
• 2) Seven less than the quotient of a number and
  six is two.
• 3) The product of five and five more than a
  number is 50.

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Practice Answer Key

• 4) The difference between thirty and twice a
  number is four.
• 5) Double the difference between a number and
  six is thirty.
• 6) The product of a number decreased by seven
  and the same number increased by five is thirteen.

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Practice Answer Key

• 7) Seven times a number decreased by eleven is
  32.
• 8) The product of a number and six decreased by
  seventeen is seven.
• 9) If twelve is added to the product of a number
  and twelve, the sum is 72.

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Practice Answer Key

• 10) Seventeen less than four times a number is
  63.

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The Problem Solving Process

• The Basics

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Strategy

• Ryans Roofing charges 50 plus 30 per hour for
  emergency roof repair. A homeowners bill was
  860 after the last storm. How long did Ryans
  Roofing spend working on the job?

Fixed Charge Hourly Charge Bill
Guess 20 hours
Let x of hours worked
50 30/hr?20 hr
650
50 30(x) 860
x 27 hours
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Basic Application Problems
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Example 1 of 8

• Evelyn paid 89.25, including 5 tax, for her
  calculator. How much did the calculator itself
  cost?

Regular Price Sales Tax Total Price
Guess 80
x 85
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Example 2 of 8

• The houses on the south side of Elm Street are
  consecutive even numbers. Wanda and Larry are
  next door neighbors and the sum of their house
  numbers is 794. Determine their house numbers.

Wandas House Larrys House 794
Numbers are 396 and 398.
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Example 3 of 8

• The top of the John Hancock Building is a
  rectangle whose length is 60 ft more than the
  width. The perimeter is 520 ft.
• Find the width and length.
• Find the area of the rectangle.

width length width length perimeter
2(width) 2(length) perimeter
Width 100 ft, Length 160 ft
Area 16,000 square feet
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Example 4 of 8

• The second angle of an architects triangle is
  three times as large as the first. The third
  angle is 30? more than the first.
• Find the measure of each angle.

Angle 1 Angle 2 Angle 3 180?
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Example 5 of 8

• A taxi ride costs 1.90 plus 1.60 for each mile
  traveled. If 18 is budgeted for a taxi ride,
  how far can you travel?

Fixed Amount Amt. Based on Miles Driven Total
Charge
Guess 10 miles
x 10.0625 miles
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Example 6 of 8

• Sarahs investment in Jet Blue stock grew 28 to
  448. How much did she invest?

Original Investment Gain in Value Current
Price
Guess 400
x 350 (original investment)
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Example 7 of 8

• Lincolns 1863 Gettysburg Address refers to the
  year 1776 as four score and seven years ago.
  Determine what length of time is a score.

1863 1776 87 years
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Example 8 of 8

• Pam scored 78 on a test that had 4 fill-ins
  worth 7 points each and 24 multiple-choice
  questions worth 3 points each. She had one
  fill-in wrong. How many multiple-choice
  questions did she get correct?

Test Score 4(7 pts) 24(3 pts)
78 3(7 pts) x(3 pts)
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Practice

• Worksheet 2

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Technical Applications
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Example 1 Washington Textbook, page 135 Ex. 3

• Several 6-volt and 12-volt batteries are arranged
  so that their individual voltages combine to
  provide a power supply of 84-volts.
• How many of each type are present if the total
  number of batteries is 10?

Total Voltage from the 6v batteries Total
Voltage from the 12v batteries 84 volts
Qty6v x 6-volts Qty12v x 12-volts 84-volts
Guess 3
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Example 2 Washington Textbook, page 135 Ex. 4

• A machinist made 132 items, some of which were
  hubs with the rest being threaded rods.
• He made 12 more hubs than threaded rods.
• How many of each kind of item did he make?

Hubs Threaded Rods 132
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Distance, Rate, Time

• Formula relating these components
• Distance Rate x Time
• D RT

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Example 3 Rate Problem

• A car travels at 40 mi/h for 2 hours along a
  road.
• A second car starts on the same route 2 hours
  later, traveling at 60 mi/h.
• How many hours will it take for the faster car to
  overtake the slower one?

Overtake Point
Starting Point
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Example 3 Rate Problem (Continued)
D RT
40 mph for 2 hrs
60 mph (starts 2 hrs after 1st car.)

• Distance slower car Distance faster car

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Example 4 Rate Problem

• A space shuttle is sent to capture an orbiting
  satellite 6,000 km ahead of its current
  position.
• The satellite travels at 27,000 km/h and the
  shuttle travels at 29,500 km/h.
• How long will it take to overtake the satellite?

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Example 4 Rate Problem (continued)
D RT
29,500 km/h
27,000 km/h
X
6,000 km

• Distance shuttle Distance satellite 6000

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Mixture Problems Intro
How much sand in each container of cement?
Cement 27 sand
Cement 30 sand
Cement 20 sand


200 lbs of cement
467 lbs of cement
667 lbs of cement
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Mixture Problem Sample 1

• On hand is 100 g of solder that is 50 tin.
• How many grams of 10 tin solder must be mixed to
  end up with solder that is 25 tin?

Solder 25 tin
Solder 50 tin
Solder 10 tin


100 grams
x grams
100 x grams
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Practice

• Worksheet Mixture Problems
• MathXL Ch 4 Section 4 Homework