Section 3 1 Writing Equations Translating Sentences into

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 - 9 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. 3 x - 12 = 20 2. 15 + x = 2 x 3. 3 b = 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 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 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. 3 m + 5 = 14 Five plus the product of three and m equals fourteen. 2. 2 a + b = c The sum of twice a and b equals c. 3. 5 x - 3 y = 22 The difference of five times x and three times y is equal to 22.

Lesson Quiz: 1. Translate into a sentence: 2 x +14 = 7 y 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