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.

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?

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 amountCost of shoes + sales tax ≤ total amount

Verbal model:

Label:

Let c = cost of shoes

Inequality:

c + .06c ≤ 32.14

Solve: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.

Example #2Example #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: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

Solve: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.

Practice: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: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 ∙ $3.00 + $2.00 ≤ $25.00

C ≤ 7 2/3

You can buy up to 7 CD’s for $25.00.