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Creating Equations

Creating Equations. i n one variable. Let’s start with building a basic linear equation. These equations involve only one variable, like x or y, and they do not involve anything complicated like powers, square roots, etc. They are written in the form ax = b where a and

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Creating Equations

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  1. Creating Equations in one variable

  2. Let’s start with building a basic linear equation. These equations involve only one variable, like x or y, and they do not involve anything complicated like powers, square roots, etc. They are written in the form ax = b where a and b are constants and a ≠ 0. Example: 6x + 7 = 42 Non example: 6x² + 8 = 58

  3. Chase has five bags of taffy and five more pieces in his pocket. Each bag contains the same number of taffy. Altogether, Chase has one hundred five pieces of taffy. How many pieces of taffy are in each bag?

  4. Chase eats five pieces of taffy from his pocket. Since he had 105 and now ate 5, he would have 105 – 5 pieces left. This means 100 pieces would be left in the bags. What you know is that you have five equal bags, which altogether have 100 pieces. You now have to split 100 into five equal parts, 100 ÷ 5 which is 20. This means that each bag has 20 pieces of taffy.

  5. Let’s try to rewrite the problem in form of an equation. 5 bags of taffy + 5 pieces of taffy = 105 pieces of taffy 5 bags + 5 = 105 Replace bags with x 5x + 5 = 105 This equation simply restates the problem using mathematical language. 5x + 5 = 105 - 5 - 5 5x = 100 Now divide both sides by 5. 5 5 x = 20 pieces of taffy

  6. Try writing an equation for this situation. Juan pays $52.35 a month for his cable bill and an additional $1.99 for each streamed movie. If his last cable bill was $68.27, how many movies did Juan watch?

  7. $52.35 (monthly charge) + $1.99 per movie = $68.27 Let’s replace per movie with x. 52.35 + 1.99x = 68.27 Now solve for x. - 52.35 - 52.35 1.99x = 15.92 1.991.99 x = 8 movies

  8. Here is another word problem to try. The manager of a candy store mixes 2 types of candies to create a 25 lb. mixture of blueberry taffy and grape tootsie rolls. The grape tootsie rolls sells for $1.40 per lb. and the blueberry taffy sells for $1.65 per lb. The manager plans to sell the mix for $1.55 per lb. How many lbs. of each candy should the store have in their mix?

  9. Let x represent the tootsie rolls Let (25-x) represent the taffy Total: 25 lbs. Tootsie rolls plus taffy equals 25 lbs. x + (25-x) = 25 lbs. Now we need to include the price of each type of candy to our equations. 1.40x + 1.65(25-x) = 1.55(25) 1.40 x +41.25 – 1.65x = 38.75 Combine like terms 41.25 - .25x = 38.75 - 41.25- 41.25 - .25x = -2.5 Divide both sides by -2.5 x = 10 lbs. of tootsie rolls (25-x) = 15 lbs. of taffy

  10. On a final note…. *Read through the entire problem *Look for key words that you will need to solve the problem *Identify your variable *Create your equation *Solve your equation *Label your answer

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