Verb: “Is” indicates the location of the equal sign.Verb: “Is” indicates the location of the equal sign.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Phrase 1: “The sum of three times a number and seven” translates to 3n + 7.

Phrase 1: “The sum of three times a number and seven” translates to 3n + 7.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Phrase 2: “One less than twice the same number” translates to 2n – 1.

Phrase 2: “One less than twice the same number” translates to 2n – 1.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Word sentence: The sum of three times a number and seven is one less than twice the same number.

Equation: 3n + 7 = 2n – 1.Equation: 3n + 7 = 2n – 1.

Example 1Example 1Find a number such that five times the sum of that number and – 3 is three less than the opposite of the number.

Find a number such that five times the sum of that number and – 3 is three less than the opposite of the number.

5(n – 3) = – n – 35(n – 3) = – n – 35n – 15 = – n – 35n – 15 = – n – 3

5n + n – 15 = – n + n – 35n + n – 15 = – n + n – 36n – 15 = – 36n – 15 = – 3

n = 2n = 2

Find a number such that five times the sum of that number and – 3 is three less than the opposite of the number.

Find a number such that five times the sum of that number and – 3 is three less than the opposite of the number.

6n = 126n = 1266 66

6n – 15 = – 36n – 15 = – 36n – 15 + 15 = – 3 + 156n – 15 + 15 = – 3 + 15

Twenty-five more than seven times a number is 46 more than four times the number.

Twenty-five more than seven times a number is 46 more than four times the number.

x = 7x = 77x + 25 = 4x + 467x + 25 = 4x + 46

ExampleExample

The product of four and three less than a number is 15 less than five times the number.

The product of four and three less than a number is 15 less than five times the number.

n = 3n = 3

ExampleExample

4(n – 3) = 5n – 154(n – 3) = 5n – 15

Steps in Solving a Word Problem

Steps in Solving a Word Problem

1. Represent an unknown quantity with a variable.

2. When necessary, represent other conditions in the problem in terms of the variable.

Steps in Solving a Word Problem

Steps in Solving a Word Problem

3. Identify two equal quantities in the problem.

4. Write and solve an equation.

5. Check the answer.

The sum of two consecutive integers is 173. Find the integers.

The sum of two consecutive integers is 173. Find the integers.Let x = the smaller integer.Let x = the smaller integer.

x + (x + 1) = 173x + (x + 1) = 173Let x + 1 = the larger integer.Let x + 1 = the larger integer.

(x + x) + 1 = 173(x + x) + 1 = 1732x + 1 = 1732x + 1 = 173

Example 2Example 2

The sum of two consecutive integers is 173. Find the integers.

The sum of two consecutive integers is 173. Find the integers.

2x + 1 = 1732x + 1 = 1732x + 1 – 1 = 173 – 12x + 1 – 1 = 173 – 1

2x = 1722x = 17222 22x = 86x = 86

x + 1 = 87x + 1 = 87

11 22 33 44 55 66 77 88 99 1010 11111212 1313 1414

22 22 22 22 22 22

22 22 22 22 22 22

Find three consecutive odd integers such that three times the third is two more than five times the first.

Find three consecutive odd integers such that three times the third is two more than five times the first.Let x = the smallest integer.Let x = the smallest integer.Let x + 2 = the next consecutive odd integer.Let x + 2 = the next consecutive odd integer.Let x + 4 = the largest integer.Let x + 4 = the largest integer.

Example 3Example 3

Find three consecutive odd integers such that three times the third is two more than five times the first.

Find three consecutive odd integers such that three times the third is two more than five times the first.

3(x + 4) = 5x + 23(x + 4) = 5x + 23x + 12 = 5x + 23x + 12 = 5x + 2

3x – 3x + 12 = 5x – 3x + 23x – 3x + 12 = 5x – 3x + 2

10 = 2x10 = 2x

12 = 2x + 212 = 2x + 212 – 2 = 2x + 2 – 212 – 2 = 2x + 2 – 2

Find three consecutive odd integers such that three times the third is two more than five times the first.

Find three consecutive odd integers such that three times the third is two more than five times the first.

10 = 2x10 = 2x22 22x = 5x = 5

x + 2 = 7x + 2 = 7x + 4 = 9x + 4 = 9

If a ship is traveling at 20 knots (nautical miles per hour), how long will it take to travel 55 nautical miles?

If a ship is traveling at 20 knots (nautical miles per hour), how long will it take to travel 55 nautical miles?r t = dr t = d

20t = 5520t = 552020 2020

t = 2.75 hr.t = 2.75 hr.

Example 4Example 4

What is the speed of the wind if a plane capable of flying 400 mi./hr. takes 3 hr. to travel 1,050 mi. into a headwind?

What is the speed of the wind if a plane capable of flying 400 mi./hr. takes 3 hr. to travel 1,050 mi. into a headwind?

(r – w) t = d(r – w) t = d(400 – w) 3 = 1,050(400 – w) 3 = 1,0501200 – 3w = 1,0501200 – 3w = 1,050

1200 – 1200 – 3w = 1,050 – 12001200 – 1200 – 3w = 1,050 – 1200

Example 5Example 5

What is the speed of the wind if a plane capable of flying 400 mi./hr. takes 3 hr. to travel 1,050 mi. into a headwind?

What is the speed of the wind if a plane capable of flying 400 mi./hr. takes 3 hr. to travel 1,050 mi. into a headwind?

– 3– 3 – 3– 3

w = 50 mi./hr.w = 50 mi./hr.

1200 – 1200 – 3w = 1,050 – 12001200 – 1200 – 3w = 1,050 – 1200– 3w = – 150– 3w = – 150

Luke and Andrew paddled their canoe 22 mi. down the river in 4 hr. If the river’s current averages 1.5 mi./hr., what is their average rate in still water?

Luke and Andrew paddled their canoe 22 mi. down the river in 4 hr. If the river’s current averages 1.5 mi./hr., what is their average rate in still water?

(r + c) t = d(r + c) t = d

(r + 1.5) 4 = 22(r + 1.5) 4 = 224r + 6 = 224r + 6 = 22

Example 6Example 6

Luke and Andrew paddled their canoe 22 mi. down the river in 4 hr. If the river’s current averages 1.5 mi./hr., what is their average rate in still water?

Luke and Andrew paddled their canoe 22 mi. down the river in 4 hr. If the river’s current averages 1.5 mi./hr., what is their average rate in still water?

4r + 6 – 6 = 22 – 64r + 6 – 6 = 22 – 64r = 164r = 1644 44r = 4 mi./hr.r = 4 mi./hr.

Find two consecutive even integers such that twice the larger is four more than twice the smaller.

Find two consecutive even integers such that twice the larger is four more than twice the smaller.

ExerciseExercise

Find two consecutive integers that five times the smaller equals three times the larger.

Find two consecutive integers that five times the smaller equals three times the larger.

ExerciseExercise

After rowing down the stream in 4 hr., the students were able to row back up the stream in 6 hr. If the stream flows at 1 mi./hr., how fast can the students row their boat in still water?

After rowing down the stream in 4 hr., the students were able to row back up the stream in 6 hr. If the stream flows at 1 mi./hr., how fast can the students row their boat in still water?

ExerciseExercise

Solve the formula d = r t for the variable t and then for the variable r.

Solve the formula d = r t for the variable t and then for the variable r.

ExerciseExercise