Linear Inequalities

Linear Inequalities Word Problems


Consider two successive even numbers. If 10 is subtracted from 4 times the smaller one, then the resulting value is smaller than 2 times the larger one. What is the maximum possible value of the sum of the two successive even numbers?

Adam took an exam with 2020 questions, and answered all of the 2020 questions. He gets 55 points for a right answer and 22 points taken off for a wrong answer. If Adam's score in the exam is between 4545 and 8080 exclusive, what is the difference between the maximum possible number of right answers (M)(M) and minimum possible number of right answers (m)?(m)?

A pair of jeans at Kim's Clothing which was priced 3030% above the merchant's cost is now on sale for 2020% off. At the sale price, the profit margin per unit is at least $77. If the merchant's cost of a pair of jeans is at least $xx, what is xx?

Let 200n(400n)200n(400-n) represent the total revenue (in dollars) of a company from selling nn units of the machine they produce, where 0n200.0\le n \le 200. If it costs 3000030000 dollars to produce one unit of the machine and the company wants their profit to be at least 26250002625000 dollars, what is the range of the number of units they need to sell?

The results of Richard's first two math tests are 8181 and 8484 points, respectively. What is the minimum score he can achieve on the third test in order to obtain an average of at least 8484 points for all three tests?


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