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: 1.Verbal model 2.Labels 3.Inequality 4.Solve 5.Answer the question Steps to follow: 1.Verbal model 2.Labels 3.Inequality 4.Solve 5.Answer the question

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

Solve: c +.06 c ≤ c ≤ 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.

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?

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

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

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?

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