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6.2 Problem solving using inequalities

6.2 Problem solving using inequalities. Write and use a linear inequality as a model of a real-life problem. You have $32.14 in your pocket that you want to spend on a new pair of shoes. If sales tax is 6%, what’s the most your shoes can cost before tax?. Steps to follow: Verbal model

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6.2 Problem solving using inequalities

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  1. 6.2 Problem solving using inequalities Write and use a linear inequality as a model of a real-life problem.

  2. You have $32.14 in your pocket that you want to spend on a new pair of shoes. If sales tax is 6%, what’s the most your shoes can cost before tax? Steps to follow: • Verbal model • Labels • Inequality • Solve • Answer the question

  3. Verbal model: Cost of shoes + sales tax ≤ total amount Label: Let c = cost of shoes Inequality: c + .06c≤ 32.14

  4. Solve: c + .06c≤ 32.14 1.06c ≤ 32.14 (combine c’s) c ≤ 30.32 (divide by 1.06) Answer question: Your shoes can cost up to $30.32 and have enough money to pay for them.

  5. Example #2 You have decided to sell model cars. If it cost you $2,000 to start your business plus $13.00 to produce each car, how many cars must you sell to realize a profit if you can sell each car for $18.00?

  6. Verbal model: Number of cars sold • cost per car > number of cars • cost to make car + set up expense Label: Let c = number of cars sold Inequality: 18c > 13c + 2000

  7. Solve: 18c > 13c + 2000 5c > 2000 (subtract 13c) c > 400 (divide by 5) Answer question: You will need to sell over 400 cars in order to make a profit.

  8. Practice: You need some new CD’s to copy your photos on to to send to your grandma in St. Louis. You found a great deal where you can get CD’s for $3.00 each plus a flat shipping fee of $2.00. If you have $25.00 to spend, how many CD’s can you order?

  9. Verbal model: # of CD’s ∙ cost of each CD + Shipping Rate ≤ Total Amount Label: Let C = # of CD’s purchased Inequality: C∙ $3.00 + $2.00 ≤ $25.00 Solve: C ≤ 7 2/3 Answer the question: You can buy up to 7 CD’s for $25.00.

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