Section 3.1 - Writing Equations. Translating Sentences into Equations Look for key words or phrases that represent “equal to”. The following all mean.

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Presentation transcript:

Section 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 x = 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 = 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 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 /x = weeks