Algebra

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 20 20 questions, and answered all of the 20 20 questions. He gets 5 5 points for a right answer and 2 2 points taken off for a wrong answer. If Adam's score in the exam is between 45 45 and 80 80 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 30 30 % above the merchant's cost is now on sale for 20 20 % off. At the sale price, the profit margin per unit is at least $ 7 7 . If the merchant's cost of a pair of jeans is at least $ x x , what is x x ?

Let 200 n ( 400 n ) 200n(400-n) represent the total revenue (in dollars) of a company from selling n n units of the machine they produce, where 0 n 200. 0\le n \le 200. If it costs 30000 30000 dollars to produce one unit of the machine and the company wants their profit to be at least 2625000 2625000 dollars, what is the range of the number of units they need to sell?

The results of Richard's first two math tests are 81 81 and 84 84 points, respectively. What is the minimum score he can achieve on the third test in order to obtain an average of at least 84 84 points for all three tests?

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