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Unformatted text preview: n a purse containing nickels and dimes, the ratio of nickels to dimes is 3 : 4. If there are 28 coins in all, what is the value of the dimes? (A) 60¢ (B) $1.12 (C) $1.60 (D) 12¢ (E) $1.00 2. 5. 3. www.petersons.com 174 Chapter 12 2. CONSECUTIVE INTEGER PROBLEMS
Consecutive integers are one apart and can be represented algebraically as x, x + 1, x + 2, and so on. Consecutive even and odd integers are both two apart and can be represented by x, x + 2, x + 4, and so on. Never try to represent consecutive odd integers by x, x + 1, x + 3, etc., for if x is odd, x + 1 would be even. Example: Find three consecutive odd integers whose sum is 219. Solution: Represent the integers as x, x + 2, and x + 4. Write an equation stating that their sum is 219. 3x + 6 = 219 3x = 213 x = 71, making the integers 71, 73, and 75. Exercise 2
Work out each problem. Circle the letter that appears before your answer. 1. If n + 1 is the largest of four consecutive integers, represent the sum of the four integers. (A) 4n + 10 (B) 4n – 2 (C) 4n – 4 (D) 4n – 5 (E) 4n – 8 If n is the first of two consecutive odd integers, which equation could be used to find these integers if the difference of their squares is 120? (A) (n + 1)2 – n2 = 120 (B) n2 – (n + 1)2 = 120 (C) n2 – (n + 2)2 = 120 (D) (n + 2)2 – n2 = 120 (E) [(n + 2)– n]2 = 120 Find the average of four consecutive odd integers whose sum is 112. (A) 25 (B) 29 (C) 31 (D) 28 (E) 30 4. Find the second of three consecutive integers if the sum of the first and third is 26. (A) 11 (B) 12 (C) 13 (D) 14 (E) 15 If 2x – 3 is an odd integer, find the next even integer. (A) 2x – 5 (B) 2x – 4 (C) 2x – 2 (D) 2x – 1 (E) 2x + 1 2. 5. 3. www.petersons.com Problem Solving in Algebra 175 3. AGE PROBLEMS
In solving age problems, you are usually called upon to represent a person’s age at the present time, several years from now, or several years ago. A person’s age x years from now is found by adding x to his present age. A person’s age x years ago is found by subtracting x...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
 Spring '10
 Colon
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