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Translating Word Problems into Equations: A Four-Step Guide

Learn how to translate sentences into equations, solve word problems step by step, and check the solutions for accuracy. Practice with examples and quizzes.

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Translating Word Problems into Equations: A Four-Step Guide

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  1. Section 3.1 - Writing Equations

  2. 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

  3. Translate these Sentences into Equations Twelve less than three times a number is twenty. Fifteen more than a number is equal to twice the same number. A number, b, times three is equal to six less than c. 1. 3x - 12 = 20 2. 15 + x = 2x 3. 3b = c - 6

  4. 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

  5. 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.

  6. 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

  7. 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?

  8. 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

  9. 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

  10. Translate Equations into Sentences 3m + 5 = 14 Five plus the product of three and m equals fourteen. 2a + b = c The sum of twice a and b equals c. 5x - 3y = 22 The difference of five times x and three times y is equal to 22.

  11. Lesson Quiz: Translate into a sentence: 2x +14 = 7y Translate into an equation: The quotient of 12 and a number is equal to 16. 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. The product of two and x increased by fourteen equals the product of seven and y. 2. 12/x = 16 3. 10 weeks

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