Algebra 1.9 Applications of Inequalities

The sum of two consecutive integers is no more than 209. What is the larger of the two integers?

105

To get on the top players' list, Don needs to have a minimum average score of 225 after playing four games. His scores on his first three games were 192, 214, and 250. What is the minimum score Don needs to earn on his fourth game?

244

Write an inequality to model this problem? Then solve. The length of a rectangle is four times its width. If the perimeter is at most 130 centimeters, what is the greatest possible value for the width?

2w+2⋅(4w)≤130 w≤13cm

Write an inequality to model this problem? Then solve. The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?

2w+2⋅(5w)≤96 w≤8cm

Write an inequality to model this problem? Then solve. Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earns $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit?

550w>4500+200w w>13 weeks

Jenny is eight years older than twice her cousin Sue's age. The sum of their ages is less than 32. What is the greatest age that Sue could be?

7 years old

Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30. What is the greatest age Brooke could be?

8 years old

Write an inequality to model this problem? Then solve. Eduardo started a business selling sporting goods. He spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. He earns $850 per week in sales. What is the minimum number of weeks it will take for Eduardo to make a profit?

850w>7500+300w w>14 weeks

The sum of two consecutive integers is at least 185. What is the smaller of the two integers?

92