Transcript Algebra Unit IV - Notes Section 3.1

Section 3.1 Writing Equations
Translating Sentences into
Equations
Look for key words or phrases that represent “equal to”. The
following all mean “equal to”:
-is
- is equal to
- in as much as
- equals
- is the same as
- is identical to
Also, look for the unknown. It will be represented by a variable.
Example - Translate: Nine times a number subtracted from 95
equals 37.
95 - 9x = 37
Translate these Sentences into
Equations
1. Twelve less than three times a number is twenty.
2. Fifteen more than a number is equal to twice the same
number.
3. A number, b, times three is equal to six less than c.
1. 3x - 12 = 20
2. 15 + x = 2x
3. 3b = c - 6
Four-Step Problem Solving
Plan
Step One - Explore the problem
Step Two - Plan the solution
Step Three - Solve the problem
Step Four - Examine the solution
Step One - Explore the Problem
Read the word problem carefully and explore what it is
about:
•Identify what information is given.
•Identify what you are asked to find - this will be the
variable.
Step Two - Plan the Solution
•Choose a variable to represent the unknown in the
problem. This is called defining the variable.
•Use the information from step one to write an equation
to model the situation
Step Three - Solve the Equation
•Isolate the variable on one side of the equation.
Step Four - Examine the Solution
•Does the answer make sense?
•Does it fit the information in the problem?
Example Word Problem A popular jellybean manufacturer produces 1,250,000
jellybeans per hour. How many hours does it take them to
produce 10,000,000 jellybeans?
Step One - Explore the problem
Step Two - Plan the solution
Step Three - Solve the problem
Step Four - Examine your solution
Write and solve an equation:
A 1 oz serving of chips has 140 calories. There are about 14
servings of chips in a bag. How many calories are there in a
bag of chips.
Step One - Explore
Step Two - Plan
Step Three - Solve
Step Four - Examine
Translate Equations into Sentences
1. 3m + 5 = 14
Five plus the product of three and m equals fourteen.
2. 2a + b = c
The sum of twice a and b equals c.
3. 5x - 3y = 22
The difference of five times x and three times y is equal
to 22.
Lesson Quiz:
1. Translate into a sentence: 2x +14 = 7y
2. Translate into an equation: The quotient of 12 and a
number is equal to 16.
3. Use the four-step plan to solve the following word
problem:
You have $250 in the bank. After how many weeks will
you have $500 in the if you save $25 per week.
1. The product of two and x increased by fourteen equals
the product of seven and y.
2. 12/x = 16
3. 10 weeks