3.1 Writing Equations

WARM UPWrite the following verbal expressions as

algebraic expressions: 1) The difference of twice a number x and 4. 2) 3 times a number y less than twice the

sum of a number x and 5 Write the following algebraic expressions as a

verbal expression. 3)    3 + 4n 4)    5 (x + 1) – 12

What is the difference between writing an algebraic expression and writing an equation?

Requires having equality in an equation or equals sign to say two expressions are the same

Equations have = signs Expressions do not (2 expressions can

become an equation)

Translate each sentence into an equation.

1)     Five times the number a is equal to three time the sum of b and c.

2)     Nine times y subtracted from 95 equals 37.

3)     The product of five and the sum of m and n is the same as seven times n.

4)     Two times a number t decreased by 8 is identical to seventy.

5a = 3(b+c)

95 – 9y = 37

5(m + n) = 7n

2t – 8 = 70

Four-Step Problem Solving Plan  

EXAMPLE: Today, 2,000,000 gallons of ice cream are produced in the United States each day. How many days can 40,000,000 gallons of ice cream be produced in the United States?STEP 1: EXPLORE THE PROBLEM

•Read the problem carefully•Identify what information is given•Identify what you are asked to find

  

     

STEP 2: PLAN THE SOLUTION

•Choose a strategy to solve the problemSTRATEGY #1: Write an Equation:

•Define a Variable: choose a variable (letter) to represent unknown numbers in the problem

 

 

Know: 2,000,000 gallons of ice cream are produced in US each day.

Want to Know: how many days it will take to produce 40,000,000 gallons of ice creamLet d represent the number of days needed to produce the ice cream.

 

2,000,000 * d = 40,000,000

STEP 3: SOLVE THE PROBLEM

•Use the strategy from Step 2 to solve the problem

 

STEP 4 EXAMINE THE SOLUTION

•Check your solution in relation to the original problem•Does it make sense?•Does it fit the information in the problem?   

 

“What number of times 2,000,000 = 40,000,000?”

2,000,000d = 40,000,000

d = 20

20 days makes sense

specific type of equation that states a rule for the relationship between certain quantities

For formulas it’s important to identify all the variables.

You are defining a variable Using known quantities with

formulas we can plug them in to find others

Formulas

1)    The area of a triangle is equal to one half times the base times the height.

a.  What is the area of a triangle with base 4 and height 11?

2)   The perimeter of a rectangle equals two times the length

plus two times the width.

a. What is the perimeter of a rectangle with base 5 and height 7?

A = ½ bh

A = 22

P = 2l + 2w

P = 24

Translate each sentence into a formula:

3)   The volume of a rectangular prism (box) is the same as the product of the length, the width, and the height.

a. What is the volume of a triangle with length 4, width 3 and height 5?

4)   The volume V of a sphere is four-thirds times times the radius r of the sphere cubed.

a.   What is the volume of a sphere with radius of 4?

V = lwh

V = 60

V = 4/3 r3

V =85.33

Practice