unit 2 solving word problems1 unit 2 word problems unit 2

Unit 2 Solving Word Problems 1

Unit 2

WORD PROBLEMS

Unit 2


1 Read the problem carefully, many times if necessary.

2 Analyze the problem and identify all numbers, values, or

3 Write a formula or simple equation to solve for the unknown term.

4 Substitute all facts stated in the problem in the formula or equation

5 Complete the arithmetic required by the formula or equation

WORD PROBLEM SUGGESTIONS:


Formulas are equations that state a fact or a rule relating two or more variables.You can solve a formula for any of its variables using the rules for solvingequations.

Example 1: F=9/5C +32 Temperature

Example 2: d=r*t Distance


Example 1

• If the temperature in Bangkok is 37 degrees Centigrade; what is the temperature expressed in Fahrenheit?

• F=9/5 C + 32• F= (1.8 * 37) +32 (do multiplication)• F= 66.6 + 32 (do addition)• F= 98.6


Example 2

It took me two and one half hours to drive from Bangkok to Pataya

at an average speed of 50 kilometers per hour. How far did I drive

to get to Pataya?

d = r*t

d = 50*2.5

d = 125 kilometers


Another Example: American Baseball

Here are the records for three American baseball players for the first 20 games of the season. Let's use the formula ( x = h / t ) to see which player has the best batting average

At bats Hits

Jerry 49 9

Benny 38 8

Chen Lin 64 13


Example 3 cont’d

Benny has the best batting average of the three players

At bats Hits Average

Jerry 49 9

0.184

Benny 38 8

0.211

Chen Lin 64 13

0.203


Rule 1

Terms of an Equation:The terms on both sides

of the = sign in an equation must always be equal in number, value or quantity, this equality will not change if the these four criteria, are met.

a. The same number is added to both the left and right sides of the = sign

b. The same number is subtracted from both the left and right sides of the = sign

c. If both the left and right sides of the = sign are multiplied by the same number.

d. If both the left and right sides of the = sign are divided by the same number.


Equations Rule 1 20 + 40 = 60

the same number 5 5

added 25 + 40 = 65

subtracted 15 + 40 = 55

multiplied 100 + 200 = 300

divided 4 + 8 = 12


Practiceif x = 4

then: x + 7 = 11

x-3 = 1

2x = 8

5x-2 = 18

5x = 20

x-9 = -5

3x+2 = 14

x/2 = 2

x/4+5 = 6


PracticeExample x-7 = 13add +7 = +7

x = 20

Example x+18 = 45subtract -18 = -18

x = 27

Example 3x = 24divide 3x/3 = 24/3

x = 8


PracticeExample x/4 = 8multiply x/4(4) = 8 x 4

x = 32

Example 5x+3x = 24combine 8x = 24divide by 8 x = 3

Example 7x = 15+2xsubtract 2x = 2x

5x = 15divide by 5 x = 3


Practicex+11 = 20

subtract 11 = 11

x = 9

15x = 54-3x

add 3x = 3x

15x+3x = 54

divide by 18 18x = 54

x = 3

4x-4 = 28

add 4 = 4

4x = 28+4

4x = 32

divide by 4 x = 8


5x+3 = 13-x

add x 5x+3+x = 13

subtract 3 5x+x = 10

combine 6x = 10

divide by 6 x = 10/6x = 1 2/3

2k = 5k-8add 8 2k+8 = 5k

subtract 2k 8 = 3kreverse: 3k = 8

divide by 3 k = 8/3


2.7k +4.3k = 19.9+72.5

combine 7k = 92.4

divide by 7 k = 13.2

(t/4.8)-9.3 = 16

add 9.3 t/4.8 = 16+9.3

Multiply by 4.8 t = 4.8(16+9.3)

t = 121.44


Rule 2Equations

To Write a Simple Equation:

Arrange the facts stated in the problem in such a manner that facts stated on the left side of the = sign are the same number, quantity, or value as the facts stated on the right side.


Step 1 Identify the facts stated in the problem that are of equal value

Arrange the facts in an equation

Bangkok Taxis charge 35 bahts for the first kilometer and 3 bahts for each additional 1/10 th (one tenth) kilometer. If the taxi meter read 95 bahts, how far did the taxi go?

Identify equal facts:

(1) Cost of first kilometer = 35b

(2)Total cost of additional 1/10 kilometers = (95-35) 60 bahts

Complete the Arithmetic - see rule 3, next


Rule 3 TO COMPLETE THE ARITHMETIC OF AN EQUATION WHEN ONE NUMBER IS UNKNOWN:

A. Write the facts stated in the problem as an equation.

B. Transfer all stated numbers to the same side of the = sign by applying Rule 2 a, b, c or d.

C. Complete the arithmetic function required by the final equation.


Bangkok Taxis charge 35 bahts for the first kilometer and 3 bahts for each additional 1/10th kilometer. If the meter reads 95 baht, how far did

the taxi go?

Identify equal facts: Cost of first kilometer = 35b

Total cost of each additional 1/10th kilometer = (95-35) 60 bahts

Equation: Total Km = 1+ ((60/10)/3) = 1+(6/3)

= 1+2 = 3 Km

Answer: Total equals 3 kilometers


Rule 4DISTRIBUTION OF A TOTAL BETWEEN TWO TERMS OF

DIFFERENT VALUE, QUANTITY, OR NUMBERS:

A. Write an equation including the terms stated in the problem.

B. Analyze the equation based on requirements of the problem.

C. Write another equation based on the analysis

D. Complete the arithmetic of the revised equation.

This type of problem may be identified by the words More than, less than, or times


Rule 4 ExampleA rectangular white board is 3

times longer than it is wide. If it were 3 meters shorter and 3 meters wider, it would be square. What is the size of the white board.

3

Step1 Write an equation including the terms

of the problem:

x = width

Step2 Analyze the equation based on the

requirements of the problem.

3x = length

9


Note: If it were shorter and wider by 3 m, it would be square. Subtract 3 from the length and add 3 to the width.

Step 3 Write a 2nd equation based on the analysis:

3x - 3 = x + 3

Step 4 Complete the arithmetic on the revised equation

3x - x = 3 +3

2x = 6

x = 3

The board is 3 meters wide and 9 meters long

6

6


Tony ate 100 burgers in five days. Each day he ate six more than the day before. How

many burgers did he eat on the first day?

Let x = the number of burgers eaten on the first day.

burgers eaten

Day 1 x

Day 2 x + 1 (6)

Day 3 x + 2 (6)

Day 4 x + 3 (6)

Day 5 x + 4 (6)

Total 5x +10 (6) = 100 burgers


Solve for x:

5x + 10 (6)

= 100

5x + 60 =100

5x =40

x = 8 burgers eaten

Day 1 8

Day 2 14

Day 3 20

Day 4 26

Day 5 32

Total 100


Everything is metric, except in the United States. When is America going to catch up?


ConverterLength Imperial-USA unit / Metric unit Metric unit / Imperial USA unit

Inch = 2.54 centimeters Centimeter = 0.39 inches

Foot = 30.48 centimeters Meter = 3.28 feet

Yard = 0.91 meters Meter = 1.09 yards

Mile = 1.61kilometers Kilometer =0.62 meters

ConverterWeight Imperial-USA unit / Metric unit Metric unit / Imperial USA unit

Ounce (weight) = 28.35 grams Gram = 0.035 ounces

Pound (lb) = 0.45 kilograms Kilogram = 2.21 pounds

UK ton (2240 lbs) 1.02 metric tons Metric ton (1000 kg) 0.98 UK tons

US ton (2000 lbs) 0.91 metric tons Metric ton (1000 kg) 1.10 US tons


ConverterArea Imperial-USA unit / Metric unit Metric unit / Imperial USA unit

Acre = 0.40 hectare Hectare =2.47 acres

Square Inch = 6.45 square centimeters Square centimeter 0.16 square inches

Square foot = 0.09 square meters Square meter = 10.76 square feet

Square Yard = 0.84 square meters Square meter = 1.20 square yards

Square Mile = 2.60 square kilometers Square kilometer = 0.39 square miles

Cubic Foot = 0.028 cubic meters Cubic meter = 35.23 cubic feet

Cubic Yard = 0.76 cubic meters Cubic meter = 1.35 cubic yards


ConverterVolume Imperial-USA unit / Metric unit Metric unit / Imperial USA unit

Teaspoon (UK) = 5.92 milliliters millilitre = 0.17 teaspoons (UK)

Teaspoon (US) = 4.93 milliliters " = 0.20 teaspoons (US)

Tablespoon (UK)= 17.76 milliliters 10 milliliter = 0.56 tablespoons (UK)

Tablespoon (US)= 14.79 milliliters " = 0.68 tablespoons (US)

Fluid ounce (UK)= 28.41 milliliters 100 milliliter = 3.52 fluid ounces (UK)

Fluid ounce (US)= 29.57 milliliters " = 3.38 fluid ounces (US)

Pint (UK) = 0.57 liters Litre = 1.76 pints (UK)

Pint (US) = 0.47 liters " = 2.11 pints (US)

Quart (UK) = 1.14 liters " = 0.88 quarts (UK)

Quart (US) = 0.95 liters " = 1.06 quarts (US)

Gallon (UK) = 4.55 liters " = 0.22 gallons (UK)

Gallon (US) = 3.79 liters " = 0.26 gallons (US)


Homework

1Majid's clothing store bought shirts for resale. He bought six

for 1,000 baht and sold them 4 for 1,000 baht.

He made 6,000 profit. How many shirts did he sell?

2Water conservation can be a big problem in some parts

of the world. If a community's

water pump drips 3 drops every second and each drop is one and one third ml (milliliters)

how much water is wasted in one day?


Homework

3Swiss cheese costs $2.00 for 1/2 kilogram. How much does 1 pound cost?

4

A 800 seat multiplex is divided into 3 theaters. There are 270 seats in theater 1 and

there are 150 more seats in theater 2 than in theater 3. How many seats in theater 2?


Homework5. Franky entered into a fish cake frying contest at Siam

University. Franky wanted to win. He practiced everyday for six days. Each day he fried 4 more fish cakes than the day before. Franky fried a total of 150 cakes in 6 days. How many fish cakes did he fron on the first day?

unit 2 solving word problems1 unit 2 word problems unit 2

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