Question

Read the scenario below. Then answer all three parts completely. Be sure to use complete sentences and/or show your work.

Naviah got a new job that requires her to commute. She drives at least 30 miles but less than 50 miles each week.

Part A. First write the compound inequality representing all possible disances in miles (x) Naviah could drive for 4 weeks.

Part B. Explain while you chose the symbols you used for the endpoints of the compound inequality in Part A.

Part C. Naviah buys at least 8 but no more than 12 gallons of gas each week. The price of gas ranged from $2.25 to $2.50 per gallon each week. Write a compound inequality to model all of the possible amounts of money (m) Naviah spends on gas each week. Show or explain all work in detail

Answer 1

Explanation:

Part A

At least 30 miles but less than 50 miles each week.

Required inequality:

• 30 ≤ x < 50

In 4 weeks:

• 120 ≤ 4x < 200

Part B

• "At least" means equal or more than 30, hence 30 ≤ x
• Less than 50, hence x < 50

Part C

At least 8 but no more than 12 gallons of gas each week, with the cost $2.25 to $2.50 per gallon.

Match the lowest and highest ends. This is converted as:

• 8*$2.25 ≤ m ≤ 12*$2.50

Simplified:

• $18 ≤ m ≤ $30