3.1 Writing Equations

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3.1 Writing Equations. WARM UP. Write 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.

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3.1 Writing Equations

WARM UP

Write 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

STEP 2: PLAN THE SOLUTION

• Identify what information is given
• Identify what you are asked to find
• Choose a strategy to solve the problem
• STRATEGY #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 cream

Let d represent the number of days needed to produce the ice cream.

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

STEP 3: SOLVE THE PROBLEM

• STEP 4 EXAMINE THE SOLUTION
• Use the strategy from Step 2 to solve the problem
• 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

Formulas
• 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
Translate each sentence into a formula:

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

Practice

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