Name:Solving Inequalities in Word Problems

Date:Fundamentals of Algebra

Directions:Write out each inequality. Solve the problem algebraically.

  1. Mr. Smith had a sum of money in a bank at the start of the school year. He had $900 in the account. He wants to have at least $200 in the account by the end of the school year. He withdraws $30 each week for his personal expenses. How many weeks can he withdraw money without going lower than $200 in his account?
  1. Three times a number increased by 4 is at least 16. What is the number?
  1. Five less than a number is at most 11. What is the number?
  1. The sum of a number and 7 is less than 19. What is the number?
  1. Twice a number decreased by 9 is greater than 11. What is the number?
  1. The sum of two consecutive positive integers is less than 19. What are the integers?
  1. The sum of two consecutive positive odd integers is at most 16. What are the integers?
  1. Three times a number increased by twice the number is greater than 125. What is the number?
  1. Five times a number decreased by 7 times the same number is at most 20. What is the number?
  1. A number decreased by 6 has a maximum value of 4. What is the number?
  1. Five less than a number is at most 11. What is the number?
  1. Three times a number increased by 4 is at least 16. What is the number?
  1. Carol weighs 3 times as much as Sue. Both weights are whole numbers. The sum of their weights is less than 160 pounds. Find the greatest possible weight in pounds for each girl.

(Use two let statements.)

  1. The length of a rectangle is 10 cm. less than 3 times its width. If the perimeter (add all sides) of the rectangle is at most 180 cm., find the greatest possible length of the rectangle.
  1. The length of a rectangle is 5 cm more than its width. The perimeter of the rectangle is at least 66 cm. Find the minimum measures of the length and the width.
  1. J. Crew charges a $10 shipping and handling fee for every internet order placed during the holidays. Mrs. Moneybags has no more than $1000. She wants to order sweaters for the whole family. Each sweater costs $29.99. If she has 30 members in her family, will she be able to buy each of them a sweater? Explain your answer.
  1. Lemon Limo Company charges $40 flat rate in addition to $50 per hour of rental of the limousine. Mr. Fancypants has no more than $2000 to spend on the limo. How many hours can he rent the limousine for his party?
  1. Darling Divas charges $100 flat rate for a birthday party and $18.00 for each child in the party. How many children can attend the party if the Susie’s mom no more than $300 to spend?
  1. The sum of three consecutive odd integers is at most 75. What are the largest possible integers that may comprise this set of three?
  1. The sum of two consecutive positive odd is at most 16. What are the integers?